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\sqrt{2-7x}=-2x
Subtract 2x from both sides of the equation.
\left(\sqrt{2-7x}\right)^{2}=\left(-2x\right)^{2}
Square both sides of the equation.
2-7x=\left(-2x\right)^{2}
Calculate \sqrt{2-7x} to the power of 2 and get 2-7x.
2-7x=\left(-2\right)^{2}x^{2}
Expand \left(-2x\right)^{2}.
2-7x=4x^{2}
Calculate -2 to the power of 2 and get 4.
2-7x-4x^{2}=0
Subtract 4x^{2} from both sides.
-4x^{2}-7x+2=0
Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
a+b=-7 ab=-4\times 2=-8
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as -4x^{2}+ax+bx+2. 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=1 b=-8
The solution is the pair that gives sum -7.
\left(-4x^{2}+x\right)+\left(-8x+2\right)
Rewrite -4x^{2}-7x+2 as \left(-4x^{2}+x\right)+\left(-8x+2\right).
-x\left(4x-1\right)-2\left(4x-1\right)
Factor out -x in the first and -2 in the second group.
\left(4x-1\right)\left(-x-2\right)
Factor out common term 4x-1 by using distributive property.
x=\frac{1}{4} x=-2
To find equation solutions, solve 4x-1=0 and -x-2=0.
\sqrt{2-7\times \frac{1}{4}}+2\times \frac{1}{4}=0
Substitute \frac{1}{4} for x in the equation \sqrt{2-7x}+2x=0.
1=0
Simplify. The value x=\frac{1}{4} does not satisfy the equation.
\sqrt{2-7\left(-2\right)}+2\left(-2\right)=0
Substitute -2 for x in the equation \sqrt{2-7x}+2x=0.
0=0
Simplify. The value x=-2 satisfies the equation.
x=-2
Equation \sqrt{2-7x}=-2x has a unique solution.