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Solve for x (complex solution)
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15=x^{2}+16x
Use the distributive property to multiply x by x+16.
x^{2}+16x=15
Swap sides so that all variable terms are on the left hand side.
x^{2}+16x-15=0
Subtract 15 from both sides.
x=\frac{-16±\sqrt{16^{2}-4\left(-15\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-16±\sqrt{256-4\left(-15\right)}}{2}
Square 16.
x=\frac{-16±\sqrt{256+60}}{2}
Multiply -4 times -15.
x=\frac{-16±\sqrt{316}}{2}
Add 256 to 60.
x=\frac{-16±2\sqrt{79}}{2}
Take the square root of 316.
x=\frac{2\sqrt{79}-16}{2}
Now solve the equation x=\frac{-16±2\sqrt{79}}{2} when ± is plus. Add -16 to 2\sqrt{79}.
x=\sqrt{79}-8
Divide -16+2\sqrt{79} by 2.
x=\frac{-2\sqrt{79}-16}{2}
Now solve the equation x=\frac{-16±2\sqrt{79}}{2} when ± is minus. Subtract 2\sqrt{79} from -16.
x=-\sqrt{79}-8
Divide -16-2\sqrt{79} by 2.
x=\sqrt{79}-8 x=-\sqrt{79}-8
The equation is now solved.
15=x^{2}+16x
Use the distributive property to multiply x by x+16.
x^{2}+16x=15
Swap sides so that all variable terms are on the left hand side.
x^{2}+16x+8^{2}=15+8^{2}
Divide 16, the coefficient of the x term, by 2 to get 8. Then add the square of 8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+16x+64=15+64
Square 8.
x^{2}+16x+64=79
Add 15 to 64.
\left(x+8\right)^{2}=79
Factor x^{2}+16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+8\right)^{2}}=\sqrt{79}
Take the square root of both sides of the equation.
x+8=\sqrt{79} x+8=-\sqrt{79}
Simplify.
x=\sqrt{79}-8 x=-\sqrt{79}-8
Subtract 8 from both sides of the equation.
15=x^{2}+16x
Use the distributive property to multiply x by x+16.
x^{2}+16x=15
Swap sides so that all variable terms are on the left hand side.
x^{2}+16x-15=0
Subtract 15 from both sides.
x=\frac{-16±\sqrt{16^{2}-4\left(-15\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-16±\sqrt{256-4\left(-15\right)}}{2}
Square 16.
x=\frac{-16±\sqrt{256+60}}{2}
Multiply -4 times -15.
x=\frac{-16±\sqrt{316}}{2}
Add 256 to 60.
x=\frac{-16±2\sqrt{79}}{2}
Take the square root of 316.
x=\frac{2\sqrt{79}-16}{2}
Now solve the equation x=\frac{-16±2\sqrt{79}}{2} when ± is plus. Add -16 to 2\sqrt{79}.
x=\sqrt{79}-8
Divide -16+2\sqrt{79} by 2.
x=\frac{-2\sqrt{79}-16}{2}
Now solve the equation x=\frac{-16±2\sqrt{79}}{2} when ± is minus. Subtract 2\sqrt{79} from -16.
x=-\sqrt{79}-8
Divide -16-2\sqrt{79} by 2.
x=\sqrt{79}-8 x=-\sqrt{79}-8
The equation is now solved.
15=x^{2}+16x
Use the distributive property to multiply x by x+16.
x^{2}+16x=15
Swap sides so that all variable terms are on the left hand side.
x^{2}+16x+8^{2}=15+8^{2}
Divide 16, the coefficient of the x term, by 2 to get 8. Then add the square of 8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+16x+64=15+64
Square 8.
x^{2}+16x+64=79
Add 15 to 64.
\left(x+8\right)^{2}=79
Factor x^{2}+16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+8\right)^{2}}=\sqrt{79}
Take the square root of both sides of the equation.
x+8=\sqrt{79} x+8=-\sqrt{79}
Simplify.
x=\sqrt{79}-8 x=-\sqrt{79}-8
Subtract 8 from both sides of the equation.