Solve for x
x = \frac{6}{5} = 1\frac{1}{5} = 1.2
x = -\frac{6}{5} = -1\frac{1}{5} = -1.2
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-25x^{2}=-36
Subtract 36 from both sides. Anything subtracted from zero gives its negation.
x^{2}=\frac{-36}{-25}
Divide both sides by -25.
x^{2}=\frac{36}{25}
Fraction \frac{-36}{-25} can be simplified to \frac{36}{25} by removing the negative sign from both the numerator and the denominator.
x=\frac{6}{5} x=-\frac{6}{5}
Take the square root of both sides of the equation.
-25x^{2}+36=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
x=\frac{0±\sqrt{0^{2}-4\left(-25\right)\times 36}}{2\left(-25\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -25 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-25\right)\times 36}}{2\left(-25\right)}
Square 0.
x=\frac{0±\sqrt{100\times 36}}{2\left(-25\right)}
Multiply -4 times -25.
x=\frac{0±\sqrt{3600}}{2\left(-25\right)}
Multiply 100 times 36.
x=\frac{0±60}{2\left(-25\right)}
Take the square root of 3600.
x=\frac{0±60}{-50}
Multiply 2 times -25.
x=-\frac{6}{5}
Now solve the equation x=\frac{0±60}{-50} when ± is plus. Reduce the fraction \frac{60}{-50} to lowest terms by extracting and canceling out 10.
x=\frac{6}{5}
Now solve the equation x=\frac{0±60}{-50} when ± is minus. Reduce the fraction \frac{-60}{-50} to lowest terms by extracting and canceling out 10.
x=-\frac{6}{5} x=\frac{6}{5}
The equation is now solved.
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Limits
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