8×2+10x-7=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=8⋅-7=-56 and whose sum is b=10.

Factor 10 out of 10x.

8×2+10(x)-7=0

Rewrite 10 as -4 plus 14

8×2+(-4+14)x-7=0

Apply the distributive property.

8×2-4x+14x-7=0

8×2-4x+14x-7=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(8×2-4x)+14x-7=0

Factor out the greatest common factor (GCF) from each group.

4x(2x-1)+7(2x-1)=0

4x(2x-1)+7(2x-1)=0

Factor the polynomial by factoring out the greatest common factor, 2x-1.

(2x-1)(4x+7)=0

(2x-1)(4x+7)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

2x-1=0

4x+7=0

Set the first factor equal to 0.

2x-1=0

Add 1 to both sides of the equation.

2x=1

Divide each term by 2 and simplify.

Divide each term in 2x=1 by 2.

2×2=12

Cancel the common factor of 2.

Cancel the common factor.

2×2=12

Divide x by 1.

x=12

x=12

x=12

x=12

Set the next factor equal to 0.

4x+7=0

Subtract 7 from both sides of the equation.

4x=-7

Divide each term by 4 and simplify.

Divide each term in 4x=-7 by 4.

4×4=-74

Cancel the common factor of 4.

Cancel the common factor.

4×4=-74

Divide x by 1.

x=-74

x=-74

Move the negative in front of the fraction.

x=-74

x=-74

x=-74

The final solution is all the values that make (2x-1)(4x+7)=0 true.

x=12,-74

Solve using the Square Root Property 8x^2+10x-7=0