# Solve using the Square Root Property 8x-1+6x^2=7

8x-1+6×2=7
Move 7 to the left side of the equation by subtracting it from both sides.
8x-1+6×2-7=0
Subtract 7 from -1.
8x+6×2-8=0
Factor the left side of the equation.
Factor 2 out of 8x+6×2-8.
Factor 2 out of 8x.
2(4x)+6×2-8=0
Factor 2 out of 6×2.
2(4x)+2(3×2)-8=0
Factor 2 out of -8.
2(4x)+2(3×2)+2(-4)=0
Factor 2 out of 2(4x)+2(3×2).
2(4x+3×2)+2(-4)=0
Factor 2 out of 2(4x+3×2)+2(-4).
2(4x+3×2-4)=0
2(4x+3×2-4)=0
Let u=x. Substitute u for all occurrences of x.
2(4u+3u2-4)=0
Factor by grouping.
Reorder terms.
2(3u2+4u-4)=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=3⋅-4=-12 and whose sum is b=4.
Factor 4 out of 4u.
2(3u2+4(u)-4)=0
Rewrite 4 as -2 plus 6
2(3u2+(-2+6)u-4)=0
Apply the distributive property.
2(3u2-2u+6u-4)=0
2(3u2-2u+6u-4)=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
2((3u2-2u)+6u-4)=0
Factor out the greatest common factor (GCF) from each group.
2(u(3u-2)+2(3u-2))=0
2(u(3u-2)+2(3u-2))=0
Factor the polynomial by factoring out the greatest common factor, 3u-2.
2((3u-2)(u+2))=0
2((3u-2)(u+2))=0
Factor.
Replace all occurrences of u with x.
2((3x-2)(x+2))=0
Remove unnecessary parentheses.
2(3x-2)(x+2)=0
2(3x-2)(x+2)=0
2(3x-2)(x+2)=0
Divide each term by 2 and simplify.
Divide each term in 2(3x-2)(x+2)=0 by 2.
2(3x-2)(x+2)2=02
Simplify 2(3x-2)(x+2)2.
Cancel the common factor of 2.
Cancel the common factor.
2(3x-2)(x+2)2=02
Divide (3x-2)(x+2) by 1.
(3x-2)(x+2)=02
(3x-2)(x+2)=02
Expand (3x-2)(x+2) using the FOIL Method.
Apply the distributive property.
3x(x+2)-2(x+2)=02
Apply the distributive property.
3x⋅x+3x⋅2-2(x+2)=02
Apply the distributive property.
3x⋅x+3x⋅2-2x-2⋅2=02
3x⋅x+3x⋅2-2x-2⋅2=02
Simplify and combine like terms.
Simplify each term.
Multiply x by x by adding the exponents.
Move x.
3(x⋅x)+3x⋅2-2x-2⋅2=02
Multiply x by x.
3×2+3x⋅2-2x-2⋅2=02
3×2+3x⋅2-2x-2⋅2=02
Multiply 2 by 3.
3×2+6x-2x-2⋅2=02
Multiply -2 by 2.
3×2+6x-2x-4=02
3×2+6x-2x-4=02
Subtract 2x from 6x.
3×2+4x-4=02
3×2+4x-4=02
3×2+4x-4=02
Divide 0 by 2.
3×2+4x-4=0
3×2+4x-4=0
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅-4=-12 and whose sum is b=4.
Factor 4 out of 4x.
3×2+4(x)-4=0
Rewrite 4 as -2 plus 6
3×2+(-2+6)x-4=0
Apply the distributive property.
3×2-2x+6x-4=0
3×2-2x+6x-4=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(3×2-2x)+6x-4=0
Factor out the greatest common factor (GCF) from each group.
x(3x-2)+2(3x-2)=0
x(3x-2)+2(3x-2)=0
Factor the polynomial by factoring out the greatest common factor, 3x-2.
(3x-2)(x+2)=0
(3x-2)(x+2)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
3x-2=0
x+2=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
3x-2=0
Add 2 to both sides of the equation.
3x=2
Divide each term by 3 and simplify.
Divide each term in 3x=2 by 3.
3×3=23
Cancel the common factor of 3.
Cancel the common factor.
3×3=23
Divide x by 1.
x=23
x=23
x=23
x=23
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x+2=0
Subtract 2 from both sides of the equation.
x=-2
x=-2
The final solution is all the values that make (3x-2)(x+2)=0 true.
x=23,-2
Solve using the Square Root Property 8x-1+6x^2=7