Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

4x^{2}-8=2x+3x^{2}
Use the distributive property to multiply x by 2+3x.
4x^{2}-8-2x=3x^{2}
Subtract 2x from both sides.
4x^{2}-8-2x-3x^{2}=0
Subtract 3x^{2} from both sides.
x^{2}-8-2x=0
Combine 4x^{2} and -3x^{2} to get x^{2}.
x^{2}-2x-8=0
Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
a+b=-2 ab=-8
To solve the equation, factor x^{2}-2x-8 using formula x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). To find a and b, set up a system to be solved.
1,-8 2,-4
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -8.
1-8=-7 2-4=-2
Calculate the sum for each pair.
a=-4 b=2
The solution is the pair that gives sum -2.
\left(x-4\right)\left(x+2\right)
Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.
x=4 x=-2
To find equation solutions, solve x-4=0 and x+2=0.
4x^{2}-8=2x+3x^{2}
Use the distributive property to multiply x by 2+3x.
4x^{2}-8-2x=3x^{2}
Subtract 2x from both sides.
4x^{2}-8-2x-3x^{2}=0
Subtract 3x^{2} from both sides.
x^{2}-8-2x=0
Combine 4x^{2} and -3x^{2} to get x^{2}.
x^{2}-2x-8=0
Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
a+b=-2 ab=1\left(-8\right)=-8
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx-8. To find a and b, set up a system to be solved.
1,-8 2,-4
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -8.
1-8=-7 2-4=-2
Calculate the sum for each pair.
a=-4 b=2
The solution is the pair that gives sum -2.
\left(x^{2}-4x\right)+\left(2x-8\right)
Rewrite x^{2}-2x-8 as \left(x^{2}-4x\right)+\left(2x-8\right).
x\left(x-4\right)+2\left(x-4\right)
Factor out x in the first and 2 in the second group.
\left(x-4\right)\left(x+2\right)
Factor out common term x-4 by using distributive property.
x=4 x=-2
To find equation solutions, solve x-4=0 and x+2=0.
4x^{2}-8=2x+3x^{2}
Use the distributive property to multiply x by 2+3x.
4x^{2}-8-2x=3x^{2}
Subtract 2x from both sides.
4x^{2}-8-2x-3x^{2}=0
Subtract 3x^{2} from both sides.
x^{2}-8-2x=0
Combine 4x^{2} and -3x^{2} to get x^{2}.
x^{2}-2x-8=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(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-8\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -2 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-2\right)±\sqrt{4-4\left(-8\right)}}{2}
Square -2.
x=\frac{-\left(-2\right)±\sqrt{4+32}}{2}
Multiply -4 times -8.
x=\frac{-\left(-2\right)±\sqrt{36}}{2}
Add 4 to 32.
x=\frac{-\left(-2\right)±6}{2}
Take the square root of 36.
x=\frac{2±6}{2}
The opposite of -2 is 2.
x=\frac{8}{2}
Now solve the equation x=\frac{2±6}{2} when ± is plus. Add 2 to 6.
x=4
Divide 8 by 2.
x=-\frac{4}{2}
Now solve the equation x=\frac{2±6}{2} when ± is minus. Subtract 6 from 2.
x=-2
Divide -4 by 2.
x=4 x=-2
The equation is now solved.
4x^{2}-8=2x+3x^{2}
Use the distributive property to multiply x by 2+3x.
4x^{2}-8-2x=3x^{2}
Subtract 2x from both sides.
4x^{2}-8-2x-3x^{2}=0
Subtract 3x^{2} from both sides.
x^{2}-8-2x=0
Combine 4x^{2} and -3x^{2} to get x^{2}.
x^{2}-2x=8
Add 8 to both sides. Anything plus zero gives itself.
x^{2}-2x+1=8+1
Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-2x+1=9
Add 8 to 1.
\left(x-1\right)^{2}=9
Factor x^{2}-2x+1. 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-1\right)^{2}}=\sqrt{9}
Take the square root of both sides of the equation.
x-1=3 x-1=-3
Simplify.
x=4 x=-2
Add 1 to both sides of the equation.