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h\left(18h-17\right)=0
Factor out h.
h=0 h=\frac{17}{18}
To find equation solutions, solve h=0 and 18h-17=0.
18h^{2}-17h=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
h=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}}}{2\times 18}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 18 for a, -17 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
h=\frac{-\left(-17\right)±17}{2\times 18}
Take the square root of \left(-17\right)^{2}.
h=\frac{17±17}{2\times 18}
The opposite of -17 is 17.
h=\frac{17±17}{36}
Multiply 2 times 18.
h=\frac{34}{36}
Now solve the equation h=\frac{17±17}{36} when ± is plus. Add 17 to 17.
h=\frac{17}{18}
Reduce the fraction \frac{34}{36} to lowest terms by extracting and canceling out 2.
h=\frac{0}{36}
Now solve the equation h=\frac{17±17}{36} when ± is minus. Subtract 17 from 17.
h=0
Divide 0 by 36.
h=\frac{17}{18} h=0
The equation is now solved.
18h^{2}-17h=0
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
\frac{18h^{2}-17h}{18}=\frac{0}{18}
Divide both sides by 18.
h^{2}-\frac{17}{18}h=\frac{0}{18}
Dividing by 18 undoes the multiplication by 18.
h^{2}-\frac{17}{18}h=0
Divide 0 by 18.
h^{2}-\frac{17}{18}h+\left(-\frac{17}{36}\right)^{2}=\left(-\frac{17}{36}\right)^{2}
Divide -\frac{17}{18}, the coefficient of the x term, by 2 to get -\frac{17}{36}. Then add the square of -\frac{17}{36} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
h^{2}-\frac{17}{18}h+\frac{289}{1296}=\frac{289}{1296}
Square -\frac{17}{36} by squaring both the numerator and the denominator of the fraction.
\left(h-\frac{17}{36}\right)^{2}=\frac{289}{1296}
Factor h^{2}-\frac{17}{18}h+\frac{289}{1296}. 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(h-\frac{17}{36}\right)^{2}}=\sqrt{\frac{289}{1296}}
Take the square root of both sides of the equation.
h-\frac{17}{36}=\frac{17}{36} h-\frac{17}{36}=-\frac{17}{36}
Simplify.
h=\frac{17}{18} h=0
Add \frac{17}{36} to both sides of the equation.