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x^{2}+5x+\frac{25}{4}=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-5±\sqrt{5^{2}-4\times \frac{25}{4}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 5 for b, and \frac{25}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-5±\sqrt{25-4\times \frac{25}{4}}}{2}
Square 5.
x=\frac{-5±\sqrt{25-25}}{2}
Multiply -4 times \frac{25}{4}.
x=\frac{-5±\sqrt{0}}{2}
Add 25 to -25.
x=-\frac{5}{2}
Take the square root of 0.
\left(x+\frac{5}{2}\right)^{2}=0
Factor x^{2}+5x+\frac{25}{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{5}{2}\right)^{2}}=\sqrt{0}
Take the square root of both sides of the equation.
x+\frac{5}{2}=0 x+\frac{5}{2}=0
Simplify.
x=-\frac{5}{2} x=-\frac{5}{2}
Subtract \frac{5}{2} from both sides of the equation.
x=-\frac{5}{2}
The equation is now solved. Solutions are the same.