Solve for x
x=8
x=0
Graph
Share
Copied to clipboard
x^{2}+2x+1+\left(x-2\right)^{2}=\left(x+1\right)\left(x+5\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1+x^{2}-4x+4=\left(x+1\right)\left(x+5\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
2x^{2}+2x+1-4x+4=\left(x+1\right)\left(x+5\right)
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}-2x+1+4=\left(x+1\right)\left(x+5\right)
Combine 2x and -4x to get -2x.
2x^{2}-2x+5=\left(x+1\right)\left(x+5\right)
Add 1 and 4 to get 5.
2x^{2}-2x+5=x^{2}+6x+5
Use the distributive property to multiply x+1 by x+5 and combine like terms.
2x^{2}-2x+5-x^{2}=6x+5
Subtract x^{2} from both sides.
x^{2}-2x+5=6x+5
Combine 2x^{2} and -x^{2} to get x^{2}.
x^{2}-2x+5-6x=5
Subtract 6x from both sides.
x^{2}-8x+5=5
Combine -2x and -6x to get -8x.
x^{2}-8x+5-5=0
Subtract 5 from both sides.
x^{2}-8x=0
Subtract 5 from 5 to get 0.
x\left(x-8\right)=0
Factor out x.
x=0 x=8
To find equation solutions, solve x=0 and x-8=0.
x^{2}+2x+1+\left(x-2\right)^{2}=\left(x+1\right)\left(x+5\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1+x^{2}-4x+4=\left(x+1\right)\left(x+5\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
2x^{2}+2x+1-4x+4=\left(x+1\right)\left(x+5\right)
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}-2x+1+4=\left(x+1\right)\left(x+5\right)
Combine 2x and -4x to get -2x.
2x^{2}-2x+5=\left(x+1\right)\left(x+5\right)
Add 1 and 4 to get 5.
2x^{2}-2x+5=x^{2}+6x+5
Use the distributive property to multiply x+1 by x+5 and combine like terms.
2x^{2}-2x+5-x^{2}=6x+5
Subtract x^{2} from both sides.
x^{2}-2x+5=6x+5
Combine 2x^{2} and -x^{2} to get x^{2}.
x^{2}-2x+5-6x=5
Subtract 6x from both sides.
x^{2}-8x+5=5
Combine -2x and -6x to get -8x.
x^{2}-8x+5-5=0
Subtract 5 from both sides.
x^{2}-8x=0
Subtract 5 from 5 to get 0.
x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-8\right)±8}{2}
Take the square root of \left(-8\right)^{2}.
x=\frac{8±8}{2}
The opposite of -8 is 8.
x=\frac{16}{2}
Now solve the equation x=\frac{8±8}{2} when ± is plus. Add 8 to 8.
x=8
Divide 16 by 2.
x=\frac{0}{2}
Now solve the equation x=\frac{8±8}{2} when ± is minus. Subtract 8 from 8.
x=0
Divide 0 by 2.
x=8 x=0
The equation is now solved.
x^{2}+2x+1+\left(x-2\right)^{2}=\left(x+1\right)\left(x+5\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+1+x^{2}-4x+4=\left(x+1\right)\left(x+5\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
2x^{2}+2x+1-4x+4=\left(x+1\right)\left(x+5\right)
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}-2x+1+4=\left(x+1\right)\left(x+5\right)
Combine 2x and -4x to get -2x.
2x^{2}-2x+5=\left(x+1\right)\left(x+5\right)
Add 1 and 4 to get 5.
2x^{2}-2x+5=x^{2}+6x+5
Use the distributive property to multiply x+1 by x+5 and combine like terms.
2x^{2}-2x+5-x^{2}=6x+5
Subtract x^{2} from both sides.
x^{2}-2x+5=6x+5
Combine 2x^{2} and -x^{2} to get x^{2}.
x^{2}-2x+5-6x=5
Subtract 6x from both sides.
x^{2}-8x+5=5
Combine -2x and -6x to get -8x.
x^{2}-8x+5-5=0
Subtract 5 from both sides.
x^{2}-8x=0
Subtract 5 from 5 to get 0.
x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}
Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-8x+16=16
Square -4.
\left(x-4\right)^{2}=16
Factor x^{2}-8x+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-4\right)^{2}}=\sqrt{16}
Take the square root of both sides of the equation.
x-4=4 x-4=-4
Simplify.
x=8 x=0
Add 4 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}