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Simplifying -4r(r + 6) = -63 Reorder the terms: -4r(6 + r) = -63 (6 * -4r + r * -4r) = -63 (-24r + -4r2) = -63 Solving -24r + -4r2 = -63 Solving for variable 'r'. Reorder the terms: 63 + -24r + -4r2 = -63 + 63 Combine like terms: -63 + 63 = 0 63 + -24r + -4r2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -15.75 + 6r + r2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + 6r + 15.75 + r2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + 6r + r2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + 6r + r2 = 0 + 15.75 6r + r2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 6r + r2 = 15.75 The r term is 6r. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6r + 9 + r2 = 15.75 + 9 Reorder the terms: 9 + 6r + r2 = 15.75 + 9 Combine like terms: 15.75 + 9 = 24.75 9 + 6r + r2 = 24.75 Factor a perfect square on the left side: (r + 3)(r + 3) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (r + 3) equal to 4.974937186 and -4.974937186.Subproblem 1
r + 3 = 4.974937186 Simplifying r + 3 = 4.974937186 Reorder the terms: 3 + r = 4.974937186 Solving 3 + r = 4.974937186 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 4.974937186 + -3 Combine like terms: 3 + -3 = 0 0 + r = 4.974937186 + -3 r = 4.974937186 + -3 Combine like terms: 4.974937186 + -3 = 1.974937186 r = 1.974937186 Simplifying r = 1.974937186Subproblem 2
r + 3 = -4.974937186 Simplifying r + 3 = -4.974937186 Reorder the terms: 3 + r = -4.974937186 Solving 3 + r = -4.974937186 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -4.974937186 + -3 Combine like terms: 3 + -3 = 0 0 + r = -4.974937186 + -3 r = -4.974937186 + -3 Combine like terms: -4.974937186 + -3 = -7.974937186 r = -7.974937186 Simplifying r = -7.974937186Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.974937186, -7.974937186}
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