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Solve by completing the square.\newlineh2−30h=41h^2 - 30h = 41\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____

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Q. Solve by completing the square.\newlineh2−30h=41h^2 - 30h = 41\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____
  1. Rewrite in standard form: Write the equation in the form of h2+bh=ch^2 + bh = c. We have the equation h2−30h=41h^2 - 30h = 41.
  2. Move constant term: Move the constant term to the other side of the equation.\newlineh2−30h+(302)2=41+(302)2h^2 - 30h + \left(\frac{30}{2}\right)^2 = 41 + \left(\frac{30}{2}\right)^2
  3. Complete the square: Complete the square by adding (302)2(\frac{30}{2})^2 to both sides of the equation.\newlineh2−30h+225=41+225h^2 − 30h + 225 = 41 + 225
  4. Simplify equation: Simplify both sides of the equation. h2−30h+225=266h^2 - 30h + 225 = 266
  5. Factor left side: Factor the left side of the equation.\newline(h−15)2=266(h - 15)^2 = 266
  6. Take square root: Take the square root of both sides of the equation.\newline(h−15)2=±266\sqrt{(h - 15)^2} = \pm\sqrt{266}\newlineh−15=±266h - 15 = \pm\sqrt{266}
  7. Solve for h: Solve for h by adding 1515 to both sides of the equation.h=15±266h = 15 \pm \sqrt{266}
  8. Calculate decimal values: Calculate the approximate decimal values of hh, rounded to the nearest hundredth.h≈15+266≈15+16.31≈31.31h \approx 15 + \sqrt{266} \approx 15 + 16.31 \approx 31.31h≈15−266≈15−16.31≈−1.31h \approx 15 - \sqrt{266} \approx 15 - 16.31 \approx -1.31

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