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Simplifying 0.6q2 + -84q + 30.000 = 0 Reorder the terms: 30.000 + -84q + 0.6q2 = 0 Solving 30.000 + -84q + 0.6q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. 50 + -140q + q2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -140q + -50 + q2 = 0 + -50 Reorder the terms: 50 + -50 + -140q + q2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -140q + q2 = 0 + -50 -140q + q2 = 0 + -50 Combine like terms: 0 + -50 = -50 -140q + q2 = -50 The q term is -140q. Take half its coefficient (-70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. -140q + 4900 + q2 = -50 + 4900 Reorder the terms: 4900 + -140q + q2 = -50 + 4900 Combine like terms: -50 + 4900 = 4850 4900 + -140q + q2 = 4850 Factor a perfect square on the left side: (q + -70)(q + -70) = 4850 Calculate the square root of the right side: 69.641941386 Break this problem into two subproblems by setting (q + -70) equal to 69.641941386 and -69.641941386.Subproblem 1
q + -70 = 69.641941386 Simplifying q + -70 = 69.641941386 Reorder the terms: -70 + q = 69.641941386 Solving -70 + q = 69.641941386 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + q = 69.641941386 + 70 Combine like terms: -70 + 70 = 0 0 + q = 69.641941386 + 70 q = 69.641941386 + 70 Combine like terms: 69.641941386 + 70 = 139.641941386 q = 139.641941386 Simplifying q = 139.641941386Subproblem 2
q + -70 = -69.641941386 Simplifying q + -70 = -69.641941386 Reorder the terms: -70 + q = -69.641941386 Solving -70 + q = -69.641941386 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + q = -69.641941386 + 70 Combine like terms: -70 + 70 = 0 0 + q = -69.641941386 + 70 q = -69.641941386 + 70 Combine like terms: -69.641941386 + 70 = 0.358058614 q = 0.358058614 Simplifying q = 0.358058614Solution
The solution to the problem is based on the solutions from the subproblems. q = {139.641941386, 0.358058614}
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