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Solve by completing the square.\newlineh2−24h=13h^2 - 24h = 13\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.\newlineh2−24h=13h^2 - 24h = 13\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. Write Equation in Form: Write the equation in the form of h2+bh=ch^2 + bh = c. The given equation is h2−24h=13h^2 - 24h = 13.
  2. Complete the Square: Add (b2)2(\frac{b}{2})^2 to both sides to complete the square.\newlineSince b=−24b = -24, (b2)2=(−242)2=(−12)2=144(\frac{b}{2})^2 = (\frac{-24}{2})^2 = (-12)^2 = 144.\newlineAdd 144144 to both sides of the equation.\newlineh2−24h+144=13+144h^2 − 24h + 144 = 13 + 144\newlineh2−24h+144=157h^2 − 24h + 144 = 157
  3. Factor Left Side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(h−12)2=157(h - 12)^2 = 157
  4. Take Square Root: Take the square root of both sides of the equation.\newline(h−12)2=±157\sqrt{(h - 12)^2} = \pm\sqrt{157}\newlineh−12=±157h - 12 = \pm\sqrt{157}
  5. Solve for h: Solve for h. Add 1212 to both sides of the equation. h=12±157h = 12 \pm \sqrt{157}
  6. Calculate Approximate Values: Calculate the approximate decimal values of hh, rounded to the nearest hundredth.157≈12.53\sqrt{157} \approx 12.53h≈12+12.53h \approx 12 + 12.53 or h≈12−12.53h \approx 12 - 12.53h≈24.53h \approx 24.53 or h≈−0.53h \approx -0.53

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