Skip to main content
Solve for h
Tick mark Image

Similar Problems from Web Search

Share

\left(11h-2\right)\left(11h+2\right)=0
Consider 121h^{2}-4. Rewrite 121h^{2}-4 as \left(11h\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
h=\frac{2}{11} h=-\frac{2}{11}
To find equation solutions, solve 11h-2=0 and 11h+2=0.
121h^{2}=4
Add 4 to both sides. Anything plus zero gives itself.
h^{2}=\frac{4}{121}
Divide both sides by 121.
h=\frac{2}{11} h=-\frac{2}{11}
Take the square root of both sides of the equation.
121h^{2}-4=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
h=\frac{0±\sqrt{0^{2}-4\times 121\left(-4\right)}}{2\times 121}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 121 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
h=\frac{0±\sqrt{-4\times 121\left(-4\right)}}{2\times 121}
Square 0.
h=\frac{0±\sqrt{-484\left(-4\right)}}{2\times 121}
Multiply -4 times 121.
h=\frac{0±\sqrt{1936}}{2\times 121}
Multiply -484 times -4.
h=\frac{0±44}{2\times 121}
Take the square root of 1936.
h=\frac{0±44}{242}
Multiply 2 times 121.
h=\frac{2}{11}
Now solve the equation h=\frac{0±44}{242} when ± is plus. Reduce the fraction \frac{44}{242} to lowest terms by extracting and canceling out 22.
h=-\frac{2}{11}
Now solve the equation h=\frac{0±44}{242} when ± is minus. Reduce the fraction \frac{-44}{242} to lowest terms by extracting and canceling out 22.
h=\frac{2}{11} h=-\frac{2}{11}
The equation is now solved.