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x^{2}+x-2=x+3
Use the distributive property to multiply x+2 by x-1 and combine like terms.
x^{2}+x-2-x=3
Subtract x from both sides.
x^{2}-2=3
Combine x and -x to get 0.
x^{2}=3+2
Add 2 to both sides.
x^{2}=5
Add 3 and 2 to get 5.
x=\sqrt{5} x=-\sqrt{5}
Take the square root of both sides of the equation.
x^{2}+x-2=x+3
Use the distributive property to multiply x+2 by x-1 and combine like terms.
x^{2}+x-2-x=3
Subtract x from both sides.
x^{2}-2=3
Combine x and -x to get 0.
x^{2}-2-3=0
Subtract 3 from both sides.
x^{2}-5=0
Subtract 3 from -2 to get -5.
x=\frac{0±\sqrt{0^{2}-4\left(-5\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-5\right)}}{2}
Square 0.
x=\frac{0±\sqrt{20}}{2}
Multiply -4 times -5.
x=\frac{0±2\sqrt{5}}{2}
Take the square root of 20.
x=\sqrt{5}
Now solve the equation x=\frac{0±2\sqrt{5}}{2} when ± is plus.
x=-\sqrt{5}
Now solve the equation x=\frac{0±2\sqrt{5}}{2} when ± is minus.
x=\sqrt{5} x=-\sqrt{5}
The equation is now solved.