Solving Quadratics and Trinomials

Solve by completing the square. 
 x² − 10x - 11= 0

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

• x = -2 ± √3

• x = -3 ± √2

• x = 2 ± √3

• x = 2 ± √2

Now you: What number should be added to complete the square?

Which of the following trinomials is a perfect square trinomial ?

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - _ )² = 20

What are the steps to complete the square for solving quadratics?

• The steps to complete the square for solving quadratics are: Write the quadratic equation in the form ax^2 + bx + c = 0. Move the constant term (c) to the other side of the equation. Divide the coefficient of x (b) by 2 and square it. Add the squared term to both sides of the equation. Factor the perfect square trinomial on the left side of the equation. Take the square root of both sides of the equation. Solve for x by isolating it on one side of the equation. Simplify and write the solutions.

• Write the quadratic equation in the form ax^2 + bx + c = 0. Move the constant term (c) to the other side of the equation. Divide the coefficient of x (b) by 2 and square it. Add the squared term to both sides of the equation. Factor the perfect square trinomial on the right side of the equation. Take the square root of both sides of the equation. Solve for x by isolating it on one side of the equation. Simplify and write the solutions.

• Write the quadratic equation in the form ax^2 + bx + c = 0. Move the constant term (c) to the other side of the equation. Divide the coefficient of x (b) by 2 and square it. Subtract the squared term from both sides of the equation. Factor the perfect square trinomial on the right side of the equation. Take the square root of both sides of the equation. Solve for x by isolating it on one side of the equation. Simplify and write the solutions.

• Write the quadratic equation in the form ax^2 + bx + c = 0. Move the coefficient of x (b) to the other side of the equation. Divide the constant term (c) by 2 and square it. Subtract the squared term from both sides of the equation. Factor the perfect square trinomial on the left side of the equation. Take the square root of both sides of the equation. Solve for x by isolating it on one side of the equation. Simplify and write the solutions.

How can you solve quadratics by graphing?

• Plot the points where the graph intersects the line y = 0.

• Find the x-intercepts or points where the graph intersects the x-axis.

• Use the quadratic formula to find the solutions.

• Find the y-intercepts or points where the graph intersects the y-axis.

What is the method of solving quadratics by completing the square?

• Graphing the quadratic equation

• Factoring the quadratic equation

• Manipulating the equation to create a perfect square trinomial

• Using the quadratic formula

What are the steps involved in factoring quadratics?

• The steps involved in factoring quadratics are: 1. Multiply the quadratic equation by a constant. 2. Divide the quadratic equation by a constant. 3. Add the constant term to both sides of the equation. 4. Subtract the constant term from both sides of the equation. 5. Rewrite the quadratic equation as the sum of two binomials.

• The steps involved in factoring quadratics are: 1. Square the quadratic equation. 2. Take the square root of the quadratic equation. 3. Add the square root of the constant term to both sides of the equation. 4. Subtract the square root of the constant term from both sides of the equation. 5. Rewrite the quadratic equation as the difference of two binomials.

• The steps involved in factoring quadratics are: 1. Write the quadratic equation in the form ax^2 + bx + c = 0. 2. Factor out the greatest common factor (if any). 3. Use the AC method or trial and error to find two numbers that multiply to give the constant term (c) and add up to give the coefficient of the linear term (b). 4. Rewrite the quadratic equation as the product of two binomials. 5. Set each binomial equal to zero and solve for x. The solutions will be the factors of the quadratic equation.

• The steps involved in factoring quadratics are: 1. Divide the quadratic equation by the coefficient of the linear term. 2. Multiply the quadratic equation by the coefficient of the linear term. 3. Add the coefficient of the linear term to both sides of the equation. 4. Subtract the coefficient of the linear term from both sides of the equation. 5. Rewrite the quadratic equation as the sum of two binomials.