Solve for x
x=2
x=\frac{4}{5}=0.8
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5x^{2}-14x=-8
Swap sides so that all variable terms are on the left hand side.
5x^{2}-14x+8=0
Add 8 to both sides.
a+b=-14 ab=5\times 8=40
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as 5x^{2}+ax+bx+8. To find a and b, set up a system to be solved.
-1,-40 -2,-20 -4,-10 -5,-8
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 40.
-1-40=-41 -2-20=-22 -4-10=-14 -5-8=-13
Calculate the sum for each pair.
a=-10 b=-4
The solution is the pair that gives sum -14.
\left(5x^{2}-10x\right)+\left(-4x+8\right)
Rewrite 5x^{2}-14x+8 as \left(5x^{2}-10x\right)+\left(-4x+8\right).
5x\left(x-2\right)-4\left(x-2\right)
Factor out 5x in the first and -4 in the second group.
\left(x-2\right)\left(5x-4\right)
Factor out common term x-2 by using distributive property.
x=2 x=\frac{4}{5}
To find equation solutions, solve x-2=0 and 5x-4=0.
5x^{2}-14x=-8
Swap sides so that all variable terms are on the left hand side.
5x^{2}-14x+8=0
Add 8 to both sides.
x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 5\times 8}}{2\times 5}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, -14 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-14\right)±\sqrt{196-4\times 5\times 8}}{2\times 5}
Square -14.
x=\frac{-\left(-14\right)±\sqrt{196-20\times 8}}{2\times 5}
Multiply -4 times 5.
x=\frac{-\left(-14\right)±\sqrt{196-160}}{2\times 5}
Multiply -20 times 8.
x=\frac{-\left(-14\right)±\sqrt{36}}{2\times 5}
Add 196 to -160.
x=\frac{-\left(-14\right)±6}{2\times 5}
Take the square root of 36.
x=\frac{14±6}{2\times 5}
The opposite of -14 is 14.
x=\frac{14±6}{10}
Multiply 2 times 5.
x=\frac{20}{10}
Now solve the equation x=\frac{14±6}{10} when ± is plus. Add 14 to 6.
x=2
Divide 20 by 10.
x=\frac{8}{10}
Now solve the equation x=\frac{14±6}{10} when ± is minus. Subtract 6 from 14.
x=\frac{4}{5}
Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.
x=2 x=\frac{4}{5}
The equation is now solved.
5x^{2}-14x=-8
Swap sides so that all variable terms are on the left hand side.
\frac{5x^{2}-14x}{5}=-\frac{8}{5}
Divide both sides by 5.
x^{2}-\frac{14}{5}x=-\frac{8}{5}
Dividing by 5 undoes the multiplication by 5.
x^{2}-\frac{14}{5}x+\left(-\frac{7}{5}\right)^{2}=-\frac{8}{5}+\left(-\frac{7}{5}\right)^{2}
Divide -\frac{14}{5}, the coefficient of the x term, by 2 to get -\frac{7}{5}. Then add the square of -\frac{7}{5} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{14}{5}x+\frac{49}{25}=-\frac{8}{5}+\frac{49}{25}
Square -\frac{7}{5} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{14}{5}x+\frac{49}{25}=\frac{9}{25}
Add -\frac{8}{5} to \frac{49}{25} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{7}{5}\right)^{2}=\frac{9}{25}
Factor x^{2}-\frac{14}{5}x+\frac{49}{25}. 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{7}{5}\right)^{2}}=\sqrt{\frac{9}{25}}
Take the square root of both sides of the equation.
x-\frac{7}{5}=\frac{3}{5} x-\frac{7}{5}=-\frac{3}{5}
Simplify.
x=2 x=\frac{4}{5}
Add \frac{7}{5} to both sides of the equation.
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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
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Limits
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