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Simplifying -4q2 + -20q + 315 = 0 Reorder the terms: 315 + -20q + -4q2 = 0 Solving 315 + -20q + -4q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -78.75 + 5q + q2 = 0 Move the constant term to the right: Add '78.75' to each side of the equation. -78.75 + 5q + 78.75 + q2 = 0 + 78.75 Reorder the terms: -78.75 + 78.75 + 5q + q2 = 0 + 78.75 Combine like terms: -78.75 + 78.75 = 0.00 0.00 + 5q + q2 = 0 + 78.75 5q + q2 = 0 + 78.75 Combine like terms: 0 + 78.75 = 78.75 5q + q2 = 78.75 The q term is 5q. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5q + 6.25 + q2 = 78.75 + 6.25 Reorder the terms: 6.25 + 5q + q2 = 78.75 + 6.25 Combine like terms: 78.75 + 6.25 = 85 6.25 + 5q + q2 = 85 Factor a perfect square on the left side: (q + 2.5)(q + 2.5) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (q + 2.5) equal to 9.219544457 and -9.219544457.Subproblem 1
q + 2.5 = 9.219544457 Simplifying q + 2.5 = 9.219544457 Reorder the terms: 2.5 + q = 9.219544457 Solving 2.5 + q = 9.219544457 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + q = 9.219544457 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + q = 9.219544457 + -2.5 q = 9.219544457 + -2.5 Combine like terms: 9.219544457 + -2.5 = 6.719544457 q = 6.719544457 Simplifying q = 6.719544457Subproblem 2
q + 2.5 = -9.219544457 Simplifying q + 2.5 = -9.219544457 Reorder the terms: 2.5 + q = -9.219544457 Solving 2.5 + q = -9.219544457 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + q = -9.219544457 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + q = -9.219544457 + -2.5 q = -9.219544457 + -2.5 Combine like terms: -9.219544457 + -2.5 = -11.719544457 q = -11.719544457 Simplifying q = -11.719544457Solution
The solution to the problem is based on the solutions from the subproblems. q = {6.719544457, -11.719544457}
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