Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

6=7\left(x+1\right)x
Multiply both sides of the equation by 14, the least common multiple of 7,2.
6=\left(7x+7\right)x
Use the distributive property to multiply 7 by x+1.
6=7x^{2}+7x
Use the distributive property to multiply 7x+7 by x.
7x^{2}+7x=6
Swap sides so that all variable terms are on the left hand side.
7x^{2}+7x-6=0
Subtract 6 from both sides.
x=\frac{-7±\sqrt{7^{2}-4\times 7\left(-6\right)}}{2\times 7}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 7 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-7±\sqrt{49-4\times 7\left(-6\right)}}{2\times 7}
Square 7.
x=\frac{-7±\sqrt{49-28\left(-6\right)}}{2\times 7}
Multiply -4 times 7.
x=\frac{-7±\sqrt{49+168}}{2\times 7}
Multiply -28 times -6.
x=\frac{-7±\sqrt{217}}{2\times 7}
Add 49 to 168.
x=\frac{-7±\sqrt{217}}{14}
Multiply 2 times 7.
x=\frac{\sqrt{217}-7}{14}
Now solve the equation x=\frac{-7±\sqrt{217}}{14} when ± is plus. Add -7 to \sqrt{217}.
x=\frac{\sqrt{217}}{14}-\frac{1}{2}
Divide -7+\sqrt{217} by 14.
x=\frac{-\sqrt{217}-7}{14}
Now solve the equation x=\frac{-7±\sqrt{217}}{14} when ± is minus. Subtract \sqrt{217} from -7.
x=-\frac{\sqrt{217}}{14}-\frac{1}{2}
Divide -7-\sqrt{217} by 14.
x=\frac{\sqrt{217}}{14}-\frac{1}{2} x=-\frac{\sqrt{217}}{14}-\frac{1}{2}
The equation is now solved.
6=7\left(x+1\right)x
Multiply both sides of the equation by 14, the least common multiple of 7,2.
6=\left(7x+7\right)x
Use the distributive property to multiply 7 by x+1.
6=7x^{2}+7x
Use the distributive property to multiply 7x+7 by x.
7x^{2}+7x=6
Swap sides so that all variable terms are on the left hand side.
\frac{7x^{2}+7x}{7}=\frac{6}{7}
Divide both sides by 7.
x^{2}+\frac{7}{7}x=\frac{6}{7}
Dividing by 7 undoes the multiplication by 7.
x^{2}+x=\frac{6}{7}
Divide 7 by 7.
x^{2}+x+\left(\frac{1}{2}\right)^{2}=\frac{6}{7}+\left(\frac{1}{2}\right)^{2}
Divide 1, the coefficient of the x term, by 2 to get \frac{1}{2}. Then add the square of \frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+x+\frac{1}{4}=\frac{6}{7}+\frac{1}{4}
Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.
x^{2}+x+\frac{1}{4}=\frac{31}{28}
Add \frac{6}{7} to \frac{1}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x+\frac{1}{2}\right)^{2}=\frac{31}{28}
Factor x^{2}+x+\frac{1}{4}. 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{1}{2}\right)^{2}}=\sqrt{\frac{31}{28}}
Take the square root of both sides of the equation.
x+\frac{1}{2}=\frac{\sqrt{217}}{14} x+\frac{1}{2}=-\frac{\sqrt{217}}{14}
Simplify.
x=\frac{\sqrt{217}}{14}-\frac{1}{2} x=-\frac{\sqrt{217}}{14}-\frac{1}{2}
Subtract \frac{1}{2} from both sides of the equation.