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Solve by completing the square.\newlineh2+16h+17=0h^2 + 16h + 17 = 0\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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Solve a quadratic equation by completing the squareright chevron icon

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Q. Solve by completing the square.\newlineh2+16h+17=0h^2 + 16h + 17 = 0\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: h2+16h+17=0h^2 + 16h + 17 = 0\newlineRewrite the equation in the form of x2+bx=−cx^2 + bx = -c.\newlineSubtract 1717 from both sides.\newlineh2+16h+17−17=0−17h^2 + 16h + 17 - 17 = 0 - 17\newlineh2+16h=−17h^2 + 16h = -17
  2. Complete the Square: h2+16h=−17h^2 + 16h = -17\newlineChoose the number to add to both sides to complete the square.\newlineSince (16/2)2=64(16/2)^2 = 64, add 6464 to both sides.\newlineh2+16h+64=−17+64h^2 + 16h + 64 = -17 + 64\newlineh2+16h+64=47h^2 + 16h + 64 = 47
  3. Factor Left Side: h2+16h+64=47h^2 + 16h + 64 = 47\newlineIdentify the equation after factoring the left side.\newlineh2+16h+64=47h^2 + 16h + 64 = 47\newline(h+8)2=47(h + 8)^2 = 47
  4. Take Square Root: h+8)2=47(h + 8)^2 = 47(\newlineIdentify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline\$\sqrt{(h + 8)^2} = \pm\sqrt{47}\)\(\newline\)h + \(8\) = \pm\sqrt{\(47\)}
  5. Isolate Variable: We found:\(\newline\)\(h + 8 = \pm\sqrt{47}\)\(\newline\)Choose the equation after isolating the variable h.\(\newline\)To isolate h, subtract \(8\) from both sides of the equation.\(\newline\)\(h + 8 - 8 = \pm\sqrt{47} - 8\)\(\newline\)\(h = -8 \pm \sqrt{47}\)
  6. Isolate Variable: We found:\(\newline\)\(h + 8 = \pm\sqrt{47}\)\(\newline\)Choose the equation after isolating the variable \(h\).\(\newline\)To isolate \(h\), subtract \(8\) from both sides of the equation.\(\newline\)\(h + 8 - 8 = \pm\sqrt{47} - 8\)\(\newline\)\(h = -8 \pm \sqrt{47}\)We have:\(\newline\)\(h = -8 \pm \sqrt{47}\)\(\newline\)What are the two values of \(h\)?\(\newline\)\(h = -8 + \sqrt{47}\) implies \(h \approx -8 + 6.86\).\(\newline\)\(h\)\(0\) implies \(h\)\(1\).\(\newline\)Values of \(h\): \(h\)\(3\), \(h\)\(4\)

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