Solve for x
x=-\frac{\sqrt{17}}{10}+\frac{1}{2}\approx 0.087689437
x=\frac{\sqrt{17}}{10}+\frac{1}{2}\approx 0.912310563
Graph
Share
Copied to clipboard
5x\times 5x+2=25x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x.
25xx+2=25x
Multiply 5 and 5 to get 25.
25x^{2}+2=25x
Multiply x and x to get x^{2}.
25x^{2}+2-25x=0
Subtract 25x from both sides.
25x^{2}-25x+2=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(-25\right)±\sqrt{\left(-25\right)^{2}-4\times 25\times 2}}{2\times 25}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, -25 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-25\right)±\sqrt{625-4\times 25\times 2}}{2\times 25}
Square -25.
x=\frac{-\left(-25\right)±\sqrt{625-100\times 2}}{2\times 25}
Multiply -4 times 25.
x=\frac{-\left(-25\right)±\sqrt{625-200}}{2\times 25}
Multiply -100 times 2.
x=\frac{-\left(-25\right)±\sqrt{425}}{2\times 25}
Add 625 to -200.
x=\frac{-\left(-25\right)±5\sqrt{17}}{2\times 25}
Take the square root of 425.
x=\frac{25±5\sqrt{17}}{2\times 25}
The opposite of -25 is 25.
x=\frac{25±5\sqrt{17}}{50}
Multiply 2 times 25.
x=\frac{5\sqrt{17}+25}{50}
Now solve the equation x=\frac{25±5\sqrt{17}}{50} when ± is plus. Add 25 to 5\sqrt{17}.
x=\frac{\sqrt{17}}{10}+\frac{1}{2}
Divide 25+5\sqrt{17} by 50.
x=\frac{25-5\sqrt{17}}{50}
Now solve the equation x=\frac{25±5\sqrt{17}}{50} when ± is minus. Subtract 5\sqrt{17} from 25.
x=-\frac{\sqrt{17}}{10}+\frac{1}{2}
Divide 25-5\sqrt{17} by 50.
x=\frac{\sqrt{17}}{10}+\frac{1}{2} x=-\frac{\sqrt{17}}{10}+\frac{1}{2}
The equation is now solved.
5x\times 5x+2=25x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x.
25xx+2=25x
Multiply 5 and 5 to get 25.
25x^{2}+2=25x
Multiply x and x to get x^{2}.
25x^{2}+2-25x=0
Subtract 25x from both sides.
25x^{2}-25x=-2
Subtract 2 from both sides. Anything subtracted from zero gives its negation.
\frac{25x^{2}-25x}{25}=-\frac{2}{25}
Divide both sides by 25.
x^{2}+\left(-\frac{25}{25}\right)x=-\frac{2}{25}
Dividing by 25 undoes the multiplication by 25.
x^{2}-x=-\frac{2}{25}
Divide -25 by 25.
x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-\frac{2}{25}+\left(-\frac{1}{2}\right)^{2}
Divide -1, the coefficient of the x term, by 2 to get -\frac{1}{2}. Then add the square of -\frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-x+\frac{1}{4}=-\frac{2}{25}+\frac{1}{4}
Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.
x^{2}-x+\frac{1}{4}=\frac{17}{100}
Add -\frac{2}{25} to \frac{1}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{1}{2}\right)^{2}=\frac{17}{100}
Factor x^{2}-x+\frac{1}{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{1}{2}\right)^{2}}=\sqrt{\frac{17}{100}}
Take the square root of both sides of the equation.
x-\frac{1}{2}=\frac{\sqrt{17}}{10} x-\frac{1}{2}=-\frac{\sqrt{17}}{10}
Simplify.
x=\frac{\sqrt{17}}{10}+\frac{1}{2} x=-\frac{\sqrt{17}}{10}+\frac{1}{2}
Add \frac{1}{2} to both sides of the equation.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}