Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

5\times 5=x\times 4x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.
25=x\times 4x
Multiply 5 and 5 to get 25.
25=x^{2}\times 4
Multiply x and x to get x^{2}.
x^{2}\times 4=25
Swap sides so that all variable terms are on the left hand side.
x^{2}=\frac{25}{4}
Divide both sides by 4.
x=\frac{5}{2} x=-\frac{5}{2}
Take the square root of both sides of the equation.
5\times 5=x\times 4x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.
25=x\times 4x
Multiply 5 and 5 to get 25.
25=x^{2}\times 4
Multiply x and x to get x^{2}.
x^{2}\times 4=25
Swap sides so that all variable terms are on the left hand side.
x^{2}\times 4-25=0
Subtract 25 from both sides.
4x^{2}-25=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\times 4\left(-25\right)}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 4\left(-25\right)}}{2\times 4}
Square 0.
x=\frac{0±\sqrt{-16\left(-25\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{0±\sqrt{400}}{2\times 4}
Multiply -16 times -25.
x=\frac{0±20}{2\times 4}
Take the square root of 400.
x=\frac{0±20}{8}
Multiply 2 times 4.
x=\frac{5}{2}
Now solve the equation x=\frac{0±20}{8} when ± is plus. Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.
x=-\frac{5}{2}
Now solve the equation x=\frac{0±20}{8} when ± is minus. Reduce the fraction \frac{-20}{8} to lowest terms by extracting and canceling out 4.
x=\frac{5}{2} x=-\frac{5}{2}
The equation is now solved.