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Solve by completing the square.\newlineh2+14h=13h^2 + 14h = 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+14h=13h^2 + 14h = 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. Rewrite Equation: Rewrite the equation in the form of h2+bh=ch^2 + bh = c. We have the equation h2+14h=13h^2 + 14h = 13. To complete the square, we need to move the constant term to the other side of the equation. Subtract 1313 from both sides. h2+14h−13=0h^2 + 14h - 13 = 0 h2+14h=13h^2 + 14h = 13
  2. Move Constant Term: Choose the number to add to both sides to complete the square.\newlineSince (142)2=49(\frac{14}{2})^2 = 49, we add 4949 to both sides.\newlineh2+14h+49=13+49h^2 + 14h + 49 = 13 + 49\newlineh2+14h+49=62h^2 + 14h + 49 = 62
  3. Complete the Square: Factor the left side of the equation.\newlineThe left side is now a perfect square trinomial.\newline(h+7)2=62(h + 7)^2 = 62
  4. Factor Left Side: Take the square root of both sides of the equation.\newline(h+7)2=±62\sqrt{(h + 7)^2} = \pm\sqrt{62}\newlineh+7=±62h + 7 = \pm\sqrt{62}
  5. Take Square Root: Solve for hh.\newlineSubtract 77 from both sides to isolate hh.\newlineh=−7±62h = -7 \pm \sqrt{62}
  6. Solve for hh: Simplify the square root and round to the nearest hundredth if necessary.62\sqrt{62} is approximately 7.877.87 (rounded to the nearest hundredth).h=−7±7.87h = -7 \pm 7.87
  7. Simplify Square Root: Find the two values of hh.h=−7+7.87h = -7 + 7.87 implies h≈0.87h \approx 0.87.h=−7−7.87h = -7 - 7.87 implies h≈−14.87h \approx -14.87.Values of hh: 0.870.87, −14.87-14.87

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