Solve for x
x=-1
x=-\frac{2}{3}\approx -0.666666667
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4x^{2}+8x+4-\left(10x^{2}+18x+8\right)=0
Use the distributive property to multiply 2x+2 by 5x+4 and combine like terms.
4x^{2}+8x+4-10x^{2}-18x-8=0
To find the opposite of 10x^{2}+18x+8, find the opposite of each term.
-6x^{2}+8x+4-18x-8=0
Combine 4x^{2} and -10x^{2} to get -6x^{2}.
-6x^{2}-10x+4-8=0
Combine 8x and -18x to get -10x.
-6x^{2}-10x-4=0
Subtract 8 from 4 to get -4.
-3x^{2}-5x-2=0
Divide both sides by 2.
a+b=-5 ab=-3\left(-2\right)=6
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as -3x^{2}+ax+bx-2. To find a and b, set up a system to be solved.
-1,-6 -2,-3
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 6.
-1-6=-7 -2-3=-5
Calculate the sum for each pair.
a=-2 b=-3
The solution is the pair that gives sum -5.
\left(-3x^{2}-2x\right)+\left(-3x-2\right)
Rewrite -3x^{2}-5x-2 as \left(-3x^{2}-2x\right)+\left(-3x-2\right).
-x\left(3x+2\right)-\left(3x+2\right)
Factor out -x in the first and -1 in the second group.
\left(3x+2\right)\left(-x-1\right)
Factor out common term 3x+2 by using distributive property.
x=-\frac{2}{3} x=-1
To find equation solutions, solve 3x+2=0 and -x-1=0.
4x^{2}+8x+4-\left(10x^{2}+18x+8\right)=0
Use the distributive property to multiply 2x+2 by 5x+4 and combine like terms.
4x^{2}+8x+4-10x^{2}-18x-8=0
To find the opposite of 10x^{2}+18x+8, find the opposite of each term.
-6x^{2}+8x+4-18x-8=0
Combine 4x^{2} and -10x^{2} to get -6x^{2}.
-6x^{2}-10x+4-8=0
Combine 8x and -18x to get -10x.
-6x^{2}-10x-4=0
Subtract 8 from 4 to get -4.
x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-6\right)\left(-4\right)}}{2\left(-6\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, -10 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-10\right)±\sqrt{100-4\left(-6\right)\left(-4\right)}}{2\left(-6\right)}
Square -10.
x=\frac{-\left(-10\right)±\sqrt{100+24\left(-4\right)}}{2\left(-6\right)}
Multiply -4 times -6.
x=\frac{-\left(-10\right)±\sqrt{100-96}}{2\left(-6\right)}
Multiply 24 times -4.
x=\frac{-\left(-10\right)±\sqrt{4}}{2\left(-6\right)}
Add 100 to -96.
x=\frac{-\left(-10\right)±2}{2\left(-6\right)}
Take the square root of 4.
x=\frac{10±2}{2\left(-6\right)}
The opposite of -10 is 10.
x=\frac{10±2}{-12}
Multiply 2 times -6.
x=\frac{12}{-12}
Now solve the equation x=\frac{10±2}{-12} when ± is plus. Add 10 to 2.
x=-1
Divide 12 by -12.
x=\frac{8}{-12}
Now solve the equation x=\frac{10±2}{-12} when ± is minus. Subtract 2 from 10.
x=-\frac{2}{3}
Reduce the fraction \frac{8}{-12} to lowest terms by extracting and canceling out 4.
x=-1 x=-\frac{2}{3}
The equation is now solved.
4x^{2}+8x+4-\left(10x^{2}+18x+8\right)=0
Use the distributive property to multiply 2x+2 by 5x+4 and combine like terms.
4x^{2}+8x+4-10x^{2}-18x-8=0
To find the opposite of 10x^{2}+18x+8, find the opposite of each term.
-6x^{2}+8x+4-18x-8=0
Combine 4x^{2} and -10x^{2} to get -6x^{2}.
-6x^{2}-10x+4-8=0
Combine 8x and -18x to get -10x.
-6x^{2}-10x-4=0
Subtract 8 from 4 to get -4.
-6x^{2}-10x=4
Add 4 to both sides. Anything plus zero gives itself.
\frac{-6x^{2}-10x}{-6}=\frac{4}{-6}
Divide both sides by -6.
x^{2}+\left(-\frac{10}{-6}\right)x=\frac{4}{-6}
Dividing by -6 undoes the multiplication by -6.
x^{2}+\frac{5}{3}x=\frac{4}{-6}
Reduce the fraction \frac{-10}{-6} to lowest terms by extracting and canceling out 2.
x^{2}+\frac{5}{3}x=-\frac{2}{3}
Reduce the fraction \frac{4}{-6} to lowest terms by extracting and canceling out 2.
x^{2}+\frac{5}{3}x+\left(\frac{5}{6}\right)^{2}=-\frac{2}{3}+\left(\frac{5}{6}\right)^{2}
Divide \frac{5}{3}, the coefficient of the x term, by 2 to get \frac{5}{6}. Then add the square of \frac{5}{6} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+\frac{5}{3}x+\frac{25}{36}=-\frac{2}{3}+\frac{25}{36}
Square \frac{5}{6} by squaring both the numerator and the denominator of the fraction.
x^{2}+\frac{5}{3}x+\frac{25}{36}=\frac{1}{36}
Add -\frac{2}{3} to \frac{25}{36} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x+\frac{5}{6}\right)^{2}=\frac{1}{36}
Factor x^{2}+\frac{5}{3}x+\frac{25}{36}. 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}{6}\right)^{2}}=\sqrt{\frac{1}{36}}
Take the square root of both sides of the equation.
x+\frac{5}{6}=\frac{1}{6} x+\frac{5}{6}=-\frac{1}{6}
Simplify.
x=-\frac{2}{3} x=-1
Subtract \frac{5}{6} from 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}