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Simplifying 4q2 + -56q = 36 Reorder the terms: -56q + 4q2 = 36 Solving -56q + 4q2 = 36 Solving for variable 'q'. Reorder the terms: -36 + -56q + 4q2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -56q + 4q2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -14q + q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -14q + q2)' equal to zero and attempt to solve: Simplifying -9 + -14q + q2 = 0 Solving -9 + -14q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -14q + 9 + q2 = 0 + 9 Reorder the terms: -9 + 9 + -14q + q2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -14q + q2 = 0 + 9 -14q + q2 = 0 + 9 Combine like terms: 0 + 9 = 9 -14q + q2 = 9 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 = 9 + 49 Reorder the terms: 49 + -14q + q2 = 9 + 49 Combine like terms: 9 + 49 = 58 49 + -14q + q2 = 58 Factor a perfect square on the left side: (q + -7)(q + -7) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (q + -7) equal to 7.615773106 and -7.615773106.Subproblem 1
q + -7 = 7.615773106 Simplifying q + -7 = 7.615773106 Reorder the terms: -7 + q = 7.615773106 Solving -7 + q = 7.615773106 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 = 7.615773106 + 7 Combine like terms: -7 + 7 = 0 0 + q = 7.615773106 + 7 q = 7.615773106 + 7 Combine like terms: 7.615773106 + 7 = 14.615773106 q = 14.615773106 Simplifying q = 14.615773106Subproblem 2
q + -7 = -7.615773106 Simplifying q + -7 = -7.615773106 Reorder the terms: -7 + q = -7.615773106 Solving -7 + q = -7.615773106 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 = -7.615773106 + 7 Combine like terms: -7 + 7 = 0 0 + q = -7.615773106 + 7 q = -7.615773106 + 7 Combine like terms: -7.615773106 + 7 = -0.615773106 q = -0.615773106 Simplifying q = -0.615773106Solution
The solution to the problem is based on the solutions from the subproblems. q = {14.615773106, -0.615773106}Solution
q = {14.615773106, -0.615773106}
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