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7xx+5=25x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.
7x^{2}+5=25x
Multiply x and x to get x^{2}.
7x^{2}+5-25x=0
Subtract 25x from both sides.
7x^{2}-25x+5=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 7\times 5}}{2\times 7}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, -25 for b, and 5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-25\right)±\sqrt{625-4\times 7\times 5}}{2\times 7}
Square -25.
x=\frac{-\left(-25\right)±\sqrt{625-28\times 5}}{2\times 7}
Multiply -4 times 7.
x=\frac{-\left(-25\right)±\sqrt{625-140}}{2\times 7}
Multiply -28 times 5.
x=\frac{-\left(-25\right)±\sqrt{485}}{2\times 7}
Add 625 to -140.
x=\frac{25±\sqrt{485}}{2\times 7}
The opposite of -25 is 25.
x=\frac{25±\sqrt{485}}{14}
Multiply 2 times 7.
x=\frac{\sqrt{485}+25}{14}
Now solve the equation x=\frac{25±\sqrt{485}}{14} when ± is plus. Add 25 to \sqrt{485}.
x=\frac{25-\sqrt{485}}{14}
Now solve the equation x=\frac{25±\sqrt{485}}{14} when ± is minus. Subtract \sqrt{485} from 25.
x=\frac{\sqrt{485}+25}{14} x=\frac{25-\sqrt{485}}{14}
The equation is now solved.
7xx+5=25x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.
7x^{2}+5=25x
Multiply x and x to get x^{2}.
7x^{2}+5-25x=0
Subtract 25x from both sides.
7x^{2}-25x=-5
Subtract 5 from both sides. Anything subtracted from zero gives its negation.
\frac{7x^{2}-25x}{7}=-\frac{5}{7}
Divide both sides by 7.
x^{2}-\frac{25}{7}x=-\frac{5}{7}
Dividing by 7 undoes the multiplication by 7.
x^{2}-\frac{25}{7}x+\left(-\frac{25}{14}\right)^{2}=-\frac{5}{7}+\left(-\frac{25}{14}\right)^{2}
Divide -\frac{25}{7}, the coefficient of the x term, by 2 to get -\frac{25}{14}. Then add the square of -\frac{25}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{25}{7}x+\frac{625}{196}=-\frac{5}{7}+\frac{625}{196}
Square -\frac{25}{14} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{25}{7}x+\frac{625}{196}=\frac{485}{196}
Add -\frac{5}{7} to \frac{625}{196} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{25}{14}\right)^{2}=\frac{485}{196}
Factor x^{2}-\frac{25}{7}x+\frac{625}{196}. 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{25}{14}\right)^{2}}=\sqrt{\frac{485}{196}}
Take the square root of both sides of the equation.
x-\frac{25}{14}=\frac{\sqrt{485}}{14} x-\frac{25}{14}=-\frac{\sqrt{485}}{14}
Simplify.
x=\frac{\sqrt{485}+25}{14} x=\frac{25-\sqrt{485}}{14}
Add \frac{25}{14} to both sides of the equation.