Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

x\left(-36x-35\right)=0
Factor out x.
x=0 x=-\frac{35}{36}
To find equation solutions, solve x=0 and -36x-35=0.
-36x^{2}-35x=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{-\left(-35\right)±\sqrt{\left(-35\right)^{2}}}{2\left(-36\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -36 for a, -35 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-35\right)±35}{2\left(-36\right)}
Take the square root of \left(-35\right)^{2}.
x=\frac{35±35}{2\left(-36\right)}
The opposite of -35 is 35.
x=\frac{35±35}{-72}
Multiply 2 times -36.
x=\frac{70}{-72}
Now solve the equation x=\frac{35±35}{-72} when ± is plus. Add 35 to 35.
x=-\frac{35}{36}
Reduce the fraction \frac{70}{-72} to lowest terms by extracting and canceling out 2.
x=\frac{0}{-72}
Now solve the equation x=\frac{35±35}{-72} when ± is minus. Subtract 35 from 35.
x=0
Divide 0 by -72.
x=-\frac{35}{36} x=0
The equation is now solved.
-36x^{2}-35x=0
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
\frac{-36x^{2}-35x}{-36}=\frac{0}{-36}
Divide both sides by -36.
x^{2}+\left(-\frac{35}{-36}\right)x=\frac{0}{-36}
Dividing by -36 undoes the multiplication by -36.
x^{2}+\frac{35}{36}x=\frac{0}{-36}
Divide -35 by -36.
x^{2}+\frac{35}{36}x=0
Divide 0 by -36.
x^{2}+\frac{35}{36}x+\left(\frac{35}{72}\right)^{2}=\left(\frac{35}{72}\right)^{2}
Divide \frac{35}{36}, the coefficient of the x term, by 2 to get \frac{35}{72}. Then add the square of \frac{35}{72} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+\frac{35}{36}x+\frac{1225}{5184}=\frac{1225}{5184}
Square \frac{35}{72} by squaring both the numerator and the denominator of the fraction.
\left(x+\frac{35}{72}\right)^{2}=\frac{1225}{5184}
Factor x^{2}+\frac{35}{36}x+\frac{1225}{5184}. 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{35}{72}\right)^{2}}=\sqrt{\frac{1225}{5184}}
Take the square root of both sides of the equation.
x+\frac{35}{72}=\frac{35}{72} x+\frac{35}{72}=-\frac{35}{72}
Simplify.
x=0 x=-\frac{35}{36}
Subtract \frac{35}{72} from both sides of the equation.