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7x^{2}+14x-3=10x-2
Use the distributive property to multiply 7x by x+2.
7x^{2}+14x-3-10x=-2
Subtract 10x from both sides.
7x^{2}+4x-3=-2
Combine 14x and -10x to get 4x.
7x^{2}+4x-3+2=0
Add 2 to both sides.
7x^{2}+4x-1=0
Add -3 and 2 to get -1.
x=\frac{-4±\sqrt{4^{2}-4\times 7\left(-1\right)}}{2\times 7}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 4 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±\sqrt{16-4\times 7\left(-1\right)}}{2\times 7}
Square 4.
x=\frac{-4±\sqrt{16-28\left(-1\right)}}{2\times 7}
Multiply -4 times 7.
x=\frac{-4±\sqrt{16+28}}{2\times 7}
Multiply -28 times -1.
x=\frac{-4±\sqrt{44}}{2\times 7}
Add 16 to 28.
x=\frac{-4±2\sqrt{11}}{2\times 7}
Take the square root of 44.
x=\frac{-4±2\sqrt{11}}{14}
Multiply 2 times 7.
x=\frac{2\sqrt{11}-4}{14}
Now solve the equation x=\frac{-4±2\sqrt{11}}{14} when ± is plus. Add -4 to 2\sqrt{11}.
x=\frac{\sqrt{11}-2}{7}
Divide -4+2\sqrt{11} by 14.
x=\frac{-2\sqrt{11}-4}{14}
Now solve the equation x=\frac{-4±2\sqrt{11}}{14} when ± is minus. Subtract 2\sqrt{11} from -4.
x=\frac{-\sqrt{11}-2}{7}
Divide -4-2\sqrt{11} by 14.
x=\frac{\sqrt{11}-2}{7} x=\frac{-\sqrt{11}-2}{7}
The equation is now solved.
7x^{2}+14x-3=10x-2
Use the distributive property to multiply 7x by x+2.
7x^{2}+14x-3-10x=-2
Subtract 10x from both sides.
7x^{2}+4x-3=-2
Combine 14x and -10x to get 4x.
7x^{2}+4x=-2+3
Add 3 to both sides.
7x^{2}+4x=1
Add -2 and 3 to get 1.
\frac{7x^{2}+4x}{7}=\frac{1}{7}
Divide both sides by 7.
x^{2}+\frac{4}{7}x=\frac{1}{7}
Dividing by 7 undoes the multiplication by 7.
x^{2}+\frac{4}{7}x+\left(\frac{2}{7}\right)^{2}=\frac{1}{7}+\left(\frac{2}{7}\right)^{2}
Divide \frac{4}{7}, the coefficient of the x term, by 2 to get \frac{2}{7}. Then add the square of \frac{2}{7} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+\frac{4}{7}x+\frac{4}{49}=\frac{1}{7}+\frac{4}{49}
Square \frac{2}{7} by squaring both the numerator and the denominator of the fraction.
x^{2}+\frac{4}{7}x+\frac{4}{49}=\frac{11}{49}
Add \frac{1}{7} to \frac{4}{49} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x+\frac{2}{7}\right)^{2}=\frac{11}{49}
Factor x^{2}+\frac{4}{7}x+\frac{4}{49}. 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{2}{7}\right)^{2}}=\sqrt{\frac{11}{49}}
Take the square root of both sides of the equation.
x+\frac{2}{7}=\frac{\sqrt{11}}{7} x+\frac{2}{7}=-\frac{\sqrt{11}}{7}
Simplify.
x=\frac{\sqrt{11}-2}{7} x=\frac{-\sqrt{11}-2}{7}
Subtract \frac{2}{7} from both sides of the equation.