Solving Quadratic Equations Given as a Binomial

Find the sum of the solutions.

5x² + 6x - 1 = 0 (use 2 decimal places)

• Use quadratic formula.

• Add the values of x.

What are the steps to solving this by completing the square? x² + 10x + 21 = 0

• Subtract 21 from both sides of the equation

• Add 25 to both sides of the equation

• Rewrite the left hand side as a (binomial)²

• Take the square root of both sides of the equation

• Subtract 5 from both sides of the equation

Answer explanation

Steps for completing the square when a=1

1st: Rewrite as x² + bx = c

2nd: Take half of b, square it, then add this to both sides.

3rd: Factor the perfect square trinomial.

4th: Take the square root of both sides and solve for both cases.

5th: Write the answer using curly braces in set notation

Order the following steps for solving quadratic equations by factoring.

• Set the quadratic equation equal to zero.

• Factor the left side.

• Set each factor equal to zero, and solve each for the variable.

• Write the answer using curly braces in set notation.

Select the solutions to the equation

4x² + 11x + 7 = 0

• x = - 1.75

• x = 6

• x = - 1

• x = 1

The quadratic function y = -2x² + 4x + 6 is pictured. What are the solutions to the equation 7.5 = -2x² + 4x + 6?

• x = 0.5

• x = 1.5

• x = 1

• x = 8

• x = 6

How many solutions does this function have?

• two

• one

• all real numbers

• no real solutions

What are the solutions to the quadratic equation?

• x = -4

• x = 1

• x = -1

• x = 2

• x = 4

Solve by the Square Root method: x² = 16

• ± 4

• ± 8

• 4i

• 8i

• -4i

The points at which a parabola intersects the x-axis are the ________________.

• quadratic roots

• vertex

• axis of symmetry

• asymptotes

• factors

The ____________ is used to determine the number of solutions to a quadratic equation.