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930=x^{2}+3x+2
Use the distributive property to multiply x+1 by x+2 and combine like terms.
x^{2}+3x+2=930
Swap sides so that all variable terms are on the left hand side.
x^{2}+3x+2-930=0
Subtract 930 from both sides.
x^{2}+3x-928=0
Subtract 930 from 2 to get -928.
x=\frac{-3±\sqrt{3^{2}-4\left(-928\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 3 for b, and -928 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-3±\sqrt{9-4\left(-928\right)}}{2}
Square 3.
x=\frac{-3±\sqrt{9+3712}}{2}
Multiply -4 times -928.
x=\frac{-3±\sqrt{3721}}{2}
Add 9 to 3712.
x=\frac{-3±61}{2}
Take the square root of 3721.
x=\frac{58}{2}
Now solve the equation x=\frac{-3±61}{2} when ± is plus. Add -3 to 61.
x=29
Divide 58 by 2.
x=-\frac{64}{2}
Now solve the equation x=\frac{-3±61}{2} when ± is minus. Subtract 61 from -3.
x=-32
Divide -64 by 2.
x=29 x=-32
The equation is now solved.
930=x^{2}+3x+2
Use the distributive property to multiply x+1 by x+2 and combine like terms.
x^{2}+3x+2=930
Swap sides so that all variable terms are on the left hand side.
x^{2}+3x=930-2
Subtract 2 from both sides.
x^{2}+3x=928
Subtract 2 from 930 to get 928.
x^{2}+3x+\left(\frac{3}{2}\right)^{2}=928+\left(\frac{3}{2}\right)^{2}
Divide 3, the coefficient of the x term, by 2 to get \frac{3}{2}. Then add the square of \frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+3x+\frac{9}{4}=928+\frac{9}{4}
Square \frac{3}{2} by squaring both the numerator and the denominator of the fraction.
x^{2}+3x+\frac{9}{4}=\frac{3721}{4}
Add 928 to \frac{9}{4}.
\left(x+\frac{3}{2}\right)^{2}=\frac{3721}{4}
Factor x^{2}+3x+\frac{9}{4}. 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+\frac{3}{2}\right)^{2}}=\sqrt{\frac{3721}{4}}
Take the square root of both sides of the equation.
x+\frac{3}{2}=\frac{61}{2} x+\frac{3}{2}=-\frac{61}{2}
Simplify.
x=29 x=-32
Subtract \frac{3}{2} from both sides of the equation.