Solve for x
x=3
x=-\frac{1}{2}=-0.5
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5=2x\left(x-2\right)+\left(x-2\right)\left(-1\right)
Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.
5=2x^{2}-4x+\left(x-2\right)\left(-1\right)
Use the distributive property to multiply 2x by x-2.
5=2x^{2}-4x-x+2
Use the distributive property to multiply x-2 by -1.
5=2x^{2}-5x+2
Combine -4x and -x to get -5x.
2x^{2}-5x+2=5
Swap sides so that all variable terms are on the left hand side.
2x^{2}-5x+2-5=0
Subtract 5 from both sides.
2x^{2}-5x-3=0
Subtract 5 from 2 to get -3.
x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 2\left(-3\right)}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -5 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-5\right)±\sqrt{25-4\times 2\left(-3\right)}}{2\times 2}
Square -5.
x=\frac{-\left(-5\right)±\sqrt{25-8\left(-3\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{-\left(-5\right)±\sqrt{25+24}}{2\times 2}
Multiply -8 times -3.
x=\frac{-\left(-5\right)±\sqrt{49}}{2\times 2}
Add 25 to 24.
x=\frac{-\left(-5\right)±7}{2\times 2}
Take the square root of 49.
x=\frac{5±7}{2\times 2}
The opposite of -5 is 5.
x=\frac{5±7}{4}
Multiply 2 times 2.
x=\frac{12}{4}
Now solve the equation x=\frac{5±7}{4} when ± is plus. Add 5 to 7.
x=3
Divide 12 by 4.
x=-\frac{2}{4}
Now solve the equation x=\frac{5±7}{4} when ± is minus. Subtract 7 from 5.
x=-\frac{1}{2}
Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.
x=3 x=-\frac{1}{2}
The equation is now solved.
5=2x\left(x-2\right)+\left(x-2\right)\left(-1\right)
Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.
5=2x^{2}-4x+\left(x-2\right)\left(-1\right)
Use the distributive property to multiply 2x by x-2.
5=2x^{2}-4x-x+2
Use the distributive property to multiply x-2 by -1.
5=2x^{2}-5x+2
Combine -4x and -x to get -5x.
2x^{2}-5x+2=5
Swap sides so that all variable terms are on the left hand side.
2x^{2}-5x=5-2
Subtract 2 from both sides.
2x^{2}-5x=3
Subtract 2 from 5 to get 3.
\frac{2x^{2}-5x}{2}=\frac{3}{2}
Divide both sides by 2.
x^{2}-\frac{5}{2}x=\frac{3}{2}
Dividing by 2 undoes the multiplication by 2.
x^{2}-\frac{5}{2}x+\left(-\frac{5}{4}\right)^{2}=\frac{3}{2}+\left(-\frac{5}{4}\right)^{2}
Divide -\frac{5}{2}, the coefficient of the x term, by 2 to get -\frac{5}{4}. Then add the square of -\frac{5}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{3}{2}+\frac{25}{16}
Square -\frac{5}{4} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{49}{16}
Add \frac{3}{2} to \frac{25}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{5}{4}\right)^{2}=\frac{49}{16}
Factor x^{2}-\frac{5}{2}x+\frac{25}{16}. 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{5}{4}\right)^{2}}=\sqrt{\frac{49}{16}}
Take the square root of both sides of the equation.
x-\frac{5}{4}=\frac{7}{4} x-\frac{5}{4}=-\frac{7}{4}
Simplify.
x=3 x=-\frac{1}{2}
Add \frac{5}{4} to both sides of the equation.
Examples
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{ 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}