# Solve using the Square Root Property -2x(x+9)-20=10

-2x(x+9)-20=10
Simplify each term.
Apply the distributive property.
-2x⋅x-2x⋅9-20=10
Multiply x by x by adding the exponents.
Move x.
-2(x⋅x)-2x⋅9-20=10
Multiply x by x.
-2×2-2x⋅9-20=10
-2×2-2x⋅9-20=10
Multiply 9 by -2.
-2×2-18x-20=10
-2×2-18x-20=10
Move 10 to the left side of the equation by subtracting it from both sides.
-2×2-18x-20-10=0
Subtract 10 from -20.
-2×2-18x-30=0
Factor -2 out of -2×2-18x-30.
Factor -2 out of -2×2.
-2×2-18x-30=0
Factor -2 out of -18x.
-2×2-2(9x)-30=0
Factor -2 out of -30.
-2×2-2(9x)-2⋅15=0
Factor -2 out of -2(x2)-2(9x).
-2(x2+9x)-2⋅15=0
Factor -2 out of -2(x2+9x)-2(15).
-2(x2+9x+15)=0
-2(x2+9x+15)=0
Divide each term by -2 and simplify.
Divide each term in -2(x2+9x+15)=0 by -2.
-2(x2+9x+15)-2=0-2
Cancel the common factor of -2.
Cancel the common factor.
-2(x2+9x+15)-2=0-2
Divide x2+9x+15 by 1.
x2+9x+15=0-2
x2+9x+15=0-2
Divide 0 by -2.
x2+9x+15=0
x2+9x+15=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=9, and c=15 into the quadratic formula and solve for x.
-9±92-4⋅(1⋅15)2⋅1
Simplify.
Simplify the numerator.
Raise 9 to the power of 2.
x=-9±81-4⋅(1⋅15)2⋅1
Multiply 15 by 1.
x=-9±81-4⋅152⋅1
Multiply -4 by 15.
x=-9±81-602⋅1
Subtract 60 from 81.
x=-9±212⋅1
x=-9±212⋅1
Multiply 2 by 1.
x=-9±212
x=-9±212
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 9 to the power of 2.
x=-9±81-4⋅(1⋅15)2⋅1
Multiply 15 by 1.
x=-9±81-4⋅152⋅1
Multiply -4 by 15.
x=-9±81-602⋅1
Subtract 60 from 81.
x=-9±212⋅1
x=-9±212⋅1
Multiply 2 by 1.
x=-9±212
Change the ± to +.
x=-9+212
Rewrite -9 as -1(9).
x=-1⋅9+212
Factor -1 out of 21.
x=-1⋅9-1(-21)2
Factor -1 out of -1(9)-1(-21).
x=-1(9-21)2
Move the negative in front of the fraction.
x=-9-212
x=-9-212
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 9 to the power of 2.
x=-9±81-4⋅(1⋅15)2⋅1
Multiply 15 by 1.
x=-9±81-4⋅152⋅1
Multiply -4 by 15.
x=-9±81-602⋅1
Subtract 60 from 81.
x=-9±212⋅1
x=-9±212⋅1
Multiply 2 by 1.
x=-9±212
Change the ± to -.
x=-9-212
Rewrite -9 as -1(9).
x=-1⋅9-212
Factor -1 out of -21.
x=-1⋅9-(21)2
Factor -1 out of -1(9)-(21).
x=-1(9+21)2
Move the negative in front of the fraction.
x=-9+212
x=-9+212
The final answer is the combination of both solutions.
x=-9-212,-9+212
The result can be shown in multiple forms.
Exact Form:
x=-9-212,-9+212
Decimal Form:
x=-2.20871215…,-6.79128784…
Solve using the Square Root Property -2x(x+9)-20=10