An equation is shown.

16x² + 10x - 27 = -6x + 5

What are the solutions to the equation?

16x² + 10x - 27 = -6x + 5

What are the solutions to the equation?

Get all terms to one side of the equation, with zero on the other side of the equal sign.

16x² + 10x - 27 = -6x + 5

16x² + 16x - 32 = 0 {added 6x and subtracted 5 from each side}

16(x² + x - 2) = 0 {factored out the common factor of 16}

x² + x - 2 = 0 {divided each side by 16}

(x + 2)(x - 1) = 0 {factored into two binomials...1st terms are x....2nd terms multiplied to get -2 and added to get 1}

x + 2 = 0 or x - 1 = 0 {since those factors multiplied to equal zero, either one could be zero}

The graph of a quadratic equation is a parabola.

16x² + 10x - 27 = -6x + 5

16x² + 16x - 32 = 0 {added 6x and subtracted 5 from each side}

16(x² + x - 2) = 0 {factored out the common factor of 16}

x² + x - 2 = 0 {divided each side by 16}

(x + 2)(x - 1) = 0 {factored into two binomials...1st terms are x....2nd terms multiplied to get -2 and added to get 1}

x + 2 = 0 or x - 1 = 0 {since those factors multiplied to equal zero, either one could be zero}

**x = -2 or x = 1**{solved each equation for x}**Ask Algebra House**The graph of a quadratic equation is a parabola.

**When you**

the x-intercepts (where the graph crosses the x-axis).There are different ways to solve a quadratic equation, such as, by factoring (as shown above), completing the square, using the quadratic formula, and by using a**solve a quadratic equation for x**, you are findingthe x-intercepts (where the graph crosses the x-axis).

__graphing calculator.__