# Solve Using the Square Root Property 6x^2-17x+13=20x^2-32 6×2-17x+13=20×2-32
Move all terms containing x to the left side of the equation.
Subtract 20×2 from both sides of the equation.
6×2-17x+13-20×2=-32
Subtract 20×2 from 6×2.
-14×2-17x+13=-32
-14×2-17x+13=-32
Move 32 to the left side of the equation by adding it to both sides.
-14×2-17x+13+32=0
-14×2-17x+45=0
Factor the left side of the equation.
Factor -1 out of -14×2-17x+45.
Factor -1 out of -14×2.
-(14×2)-17x+45=0
Factor -1 out of -17x.
-(14×2)-(17x)+45=0
Rewrite 45 as -1(-45).
-(14×2)-(17x)-1⋅-45=0
Factor -1 out of -(14×2)-(17x).
-(14×2+17x)-1⋅-45=0
Factor -1 out of -(14×2+17x)-1(-45).
-(14×2+17x-45)=0
-(14×2+17x-45)=0
Factor.
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=14⋅-45=-630 and whose sum is b=17.
Factor 17 out of 17x.
-(14×2+17(x)-45)=0
Rewrite 17 as -18 plus 35
-(14×2+(-18+35)x-45)=0
Apply the distributive property.
-(14×2-18x+35x-45)=0
-(14×2-18x+35x-45)=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
-((14×2-18x)+35x-45)=0
Factor out the greatest common factor (GCF) from each group.
-(2x(7x-9)+5(7x-9))=0
-(2x(7x-9)+5(7x-9))=0
Factor the polynomial by factoring out the greatest common factor, 7x-9.
-((7x-9)(2x+5))=0
-((7x-9)(2x+5))=0
Remove unnecessary parentheses.
-(7x-9)(2x+5)=0
-(7x-9)(2x+5)=0
-(7x-9)(2x+5)=0
Multiply each term in -(7x-9)(2x+5)=0 by -1
Multiply each term in -(7x-9)(2x+5)=0 by -1.
(-(7x-9)(2x+5))⋅-1=0⋅-1
Simplify (-(7x-9)(2x+5))⋅-1.
Simplify by multiplying through.
Apply the distributive property.
(-(7x)–9)(2x+5)⋅-1=0⋅-1
Multiply.
Multiply 7 by -1.
(-7x–9)(2x+5)⋅-1=0⋅-1
Multiply -1 by -9.
(-7x+9)(2x+5)⋅-1=0⋅-1
(-7x+9)(2x+5)⋅-1=0⋅-1
(-7x+9)(2x+5)⋅-1=0⋅-1
Expand (-7x+9)(2x+5) using the FOIL Method.
Apply the distributive property.
(-7x(2x+5)+9(2x+5))⋅-1=0⋅-1
Apply the distributive property.
(-7x(2x)-7x⋅5+9(2x+5))⋅-1=0⋅-1
Apply the distributive property.
(-7x(2x)-7x⋅5+9(2x)+9⋅5)⋅-1=0⋅-1
(-7x(2x)-7x⋅5+9(2x)+9⋅5)⋅-1=0⋅-1
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
(-7⋅2×2-7x⋅5+9(2x)+9⋅5)⋅-1=0⋅-1
Multiply -7 by 2.
(-14×2-7x⋅5+9(2x)+9⋅5)⋅-1=0⋅-1
Multiply 5 by -7.
(-14×2-35x+9(2x)+9⋅5)⋅-1=0⋅-1
Multiply 2 by 9.
(-14×2-35x+18x+9⋅5)⋅-1=0⋅-1
Multiply 9 by 5.
(-14×2-35x+18x+45)⋅-1=0⋅-1
(-14×2-35x+18x+45)⋅-1=0⋅-1
(-14×2-17x+45)⋅-1=0⋅-1
(-14×2-17x+45)⋅-1=0⋅-1
Apply the distributive property.
-14×2⋅-1-17x⋅-1+45⋅-1=0⋅-1
Simplify.
Multiply -1 by -14.
14×2-17x⋅-1+45⋅-1=0⋅-1
Multiply -1 by -17.
14×2+17x+45⋅-1=0⋅-1
Multiply 45 by -1.
14×2+17x-45=0⋅-1
14×2+17x-45=0⋅-1
14×2+17x-45=0⋅-1
Multiply 0 by -1.
14×2+17x-45=0
14×2+17x-45=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=14⋅-45=-630 and whose sum is b=17.
Factor 17 out of 17x.
14×2+17(x)-45=0
Rewrite 17 as -18 plus 35
14×2+(-18+35)x-45=0
Apply the distributive property.
14×2-18x+35x-45=0
14×2-18x+35x-45=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(14×2-18x)+35x-45=0
Factor out the greatest common factor (GCF) from each group.
2x(7x-9)+5(7x-9)=0
2x(7x-9)+5(7x-9)=0
Factor the polynomial by factoring out the greatest common factor, 7x-9.
(7x-9)(2x+5)=0
(7x-9)(2x+5)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
7x-9=0
2x+5=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
7x-9=0
Add 9 to both sides of the equation.
7x=9
Divide each term by 7 and simplify.
Divide each term in 7x=9 by 7.
7×7=97
Cancel the common factor of 7.
Cancel the common factor.
7×7=97
Divide x by 1.
x=97
x=97
x=97
x=97
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
2x+5=0
Subtract 5 from both sides of the equation.
2x=-5
Divide each term by 2 and simplify.
Divide each term in 2x=-5 by 2.
2×2=-52
Cancel the common factor of 2.
Cancel the common factor.
2×2=-52
Divide x by 1.
x=-52
x=-52
Move the negative in front of the fraction.
x=-52
x=-52
x=-52
The final solution is all the values that make (7x-9)(2x+5)=0 true.
x=97,-52
Solve Using the Square Root Property 6x^2-17x+13=20x^2-32     