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Simplifying -40 + 140q + -10q2 = 0 Solving -40 + 140q + -10q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '10'. 10(-4 + 14q + -1q2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-4 + 14q + -1q2)' equal to zero and attempt to solve: Simplifying -4 + 14q + -1q2 = 0 Solving -4 + 14q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -14q + q2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -14q + -4 + q2 = 0 + -4 Reorder the terms: 4 + -4 + -14q + q2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -14q + q2 = 0 + -4 -14q + q2 = 0 + -4 Combine like terms: 0 + -4 = -4 -14q + q2 = -4 The q term is -14q. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14q + 49 + q2 = -4 + 49 Reorder the terms: 49 + -14q + q2 = -4 + 49 Combine like terms: -4 + 49 = 45 49 + -14q + q2 = 45 Factor a perfect square on the left side: (q + -7)(q + -7) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (q + -7) equal to 6.708203933 and -6.708203933.Subproblem 1
q + -7 = 6.708203933 Simplifying q + -7 = 6.708203933 Reorder the terms: -7 + q = 6.708203933 Solving -7 + q = 6.708203933 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + q = 6.708203933 + 7 Combine like terms: -7 + 7 = 0 0 + q = 6.708203933 + 7 q = 6.708203933 + 7 Combine like terms: 6.708203933 + 7 = 13.708203933 q = 13.708203933 Simplifying q = 13.708203933Subproblem 2
q + -7 = -6.708203933 Simplifying q + -7 = -6.708203933 Reorder the terms: -7 + q = -6.708203933 Solving -7 + q = -6.708203933 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + q = -6.708203933 + 7 Combine like terms: -7 + 7 = 0 0 + q = -6.708203933 + 7 q = -6.708203933 + 7 Combine like terms: -6.708203933 + 7 = 0.291796067 q = 0.291796067 Simplifying q = 0.291796067Solution
The solution to the problem is based on the solutions from the subproblems. q = {13.708203933, 0.291796067}Solution
q = {13.708203933, 0.291796067}
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