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Simplifying -2q2 + -16q + 70 = 0 Reorder the terms: 70 + -16q + -2q2 = 0 Solving 70 + -16q + -2q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(35 + -8q + -1q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + -8q + -1q2)' equal to zero and attempt to solve: Simplifying 35 + -8q + -1q2 = 0 Solving 35 + -8q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + 8q + q2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 8q + 35 + q2 = 0 + 35 Reorder the terms: -35 + 35 + 8q + q2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 8q + q2 = 0 + 35 8q + q2 = 0 + 35 Combine like terms: 0 + 35 = 35 8q + q2 = 35 The q term is 8q. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8q + 16 + q2 = 35 + 16 Reorder the terms: 16 + 8q + q2 = 35 + 16 Combine like terms: 35 + 16 = 51 16 + 8q + q2 = 51 Factor a perfect square on the left side: (q + 4)(q + 4) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (q + 4) equal to 7.141428429 and -7.141428429.Subproblem 1
q + 4 = 7.141428429 Simplifying q + 4 = 7.141428429 Reorder the terms: 4 + q = 7.141428429 Solving 4 + q = 7.141428429 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = 7.141428429 + -4 Combine like terms: 4 + -4 = 0 0 + q = 7.141428429 + -4 q = 7.141428429 + -4 Combine like terms: 7.141428429 + -4 = 3.141428429 q = 3.141428429 Simplifying q = 3.141428429Subproblem 2
q + 4 = -7.141428429 Simplifying q + 4 = -7.141428429 Reorder the terms: 4 + q = -7.141428429 Solving 4 + q = -7.141428429 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = -7.141428429 + -4 Combine like terms: 4 + -4 = 0 0 + q = -7.141428429 + -4 q = -7.141428429 + -4 Combine like terms: -7.141428429 + -4 = -11.141428429 q = -11.141428429 Simplifying q = -11.141428429Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.141428429, -11.141428429}Solution
q = {3.141428429, -11.141428429}
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