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Solve by completing the square.\newlinew2+26w+37=0w^2 + 26w + 37 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____

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Solve a quadratic equation by completing the squareright chevron icon

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Q. Solve by completing the square.\newlinew2+26w+37=0w^2 + 26w + 37 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____
  1. Rewrite and Subtract: w2+26w+37=0w^2 + 26w + 37 = 0\newlineRewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineSubtract 3737 from both sides.\newlinew2+26w+37−37=0−37w^2 + 26w + 37 - 37 = 0 - 37\newlinew2+26w=−37w^2 + 26w = -37
  2. Complete the Square: w2+26w=−37w^2 + 26w = -37\newlineChoose the equation after completing the square.\newlineSince (26/2)2=169(26/2)^2 = 169, add 169169 to both sides.\newlinew2+26w+169=−37+169w^2 + 26w + 169 = -37 + 169\newlinew2+26w+169=132w^2 + 26w + 169 = 132
  3. Factor and Identify: w2+26w+169=132w^2 + 26w + 169 = 132\newlineIdentify the equation after factoring the left side.\newlinew2+26w+169=132w^2 + 26w + 169 = 132\newline(w+13)2=132(w + 13)^2 = 132
  4. Take Square Root: w+13)2=132(w + 13)^2 = 132(\newlineIdentify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline\$\sqrt{(w + 13)^2} = \sqrt{132}\)\(\newline\)\(w + 13 = \pm\sqrt{132}\)
  5. Isolate Variable: We found:\(\newline\)\(w + 13 = \pm\sqrt{132}\)\(\newline\)Choose the equation after isolating the variable \(w\).\(\newline\)To isolate \(w\), subtract \(13\) from both sides of the equation.\(\newline\)\(w + 13 - 13 = \pm\sqrt{132} - 13\)\(\newline\)\(w = \pm\sqrt{132} - 13\)
  6. Isolate Variable: We found:\(\newline\)\(w + 13 = \pm\sqrt{132}\)\(\newline\)Choose the equation after isolating the variable w.\(\newline\)To isolate \(w\), subtract \(13\) from both sides of the equation.\(\newline\)\(w + 13 - 13 = \pm\sqrt{132} - 13\)\(\newline\)\(w = \pm\sqrt{132} - 13\)We have:\(\newline\)\(w = \pm\sqrt{132} - 13\)\(\newline\)What are the two values of \(w\)?\(\newline\)\(w = \sqrt{132} - 13\) implies \(w \approx 11.49 - 13\).\(\newline\)\(w = -\sqrt{132} - 13\) implies \(w\)\(0\).\(\newline\)Values of \(w\): \(w\)\(2\), \(w\)\(3\)

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