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Simplifying 0.40 = 4r2 + -48r Reorder the terms: 0.40 = -48r + 4r2 Solving 0.40 = -48r + 4r2 Solving for variable 'r'. Reorder the terms: 0.40 + 48r + -4r2 = -48r + 48r + 4r2 + -4r2 Combine like terms: -48r + 48r = 0 0.40 + 48r + -4r2 = 0 + 4r2 + -4r2 0.40 + 48r + -4r2 = 4r2 + -4r2 Combine like terms: 4r2 + -4r2 = 0 0.40 + 48r + -4r2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.1 + -12r + r2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -12r + 0.1 + r2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -12r + r2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -12r + r2 = 0 + 0.1 -12r + r2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -12r + r2 = 0.1 The r term is -12r. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12r + 36 + r2 = 0.1 + 36 Reorder the terms: 36 + -12r + r2 = 0.1 + 36 Combine like terms: 0.1 + 36 = 36.1 36 + -12r + r2 = 36.1 Factor a perfect square on the left side: (r + -6)(r + -6) = 36.1 Calculate the square root of the right side: 6.008327554 Break this problem into two subproblems by setting (r + -6) equal to 6.008327554 and -6.008327554.Subproblem 1
r + -6 = 6.008327554 Simplifying r + -6 = 6.008327554 Reorder the terms: -6 + r = 6.008327554 Solving -6 + r = 6.008327554 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = 6.008327554 + 6 Combine like terms: -6 + 6 = 0 0 + r = 6.008327554 + 6 r = 6.008327554 + 6 Combine like terms: 6.008327554 + 6 = 12.008327554 r = 12.008327554 Simplifying r = 12.008327554Subproblem 2
r + -6 = -6.008327554 Simplifying r + -6 = -6.008327554 Reorder the terms: -6 + r = -6.008327554 Solving -6 + r = -6.008327554 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = -6.008327554 + 6 Combine like terms: -6 + 6 = 0 0 + r = -6.008327554 + 6 r = -6.008327554 + 6 Combine like terms: -6.008327554 + 6 = -0.008327554 r = -0.008327554 Simplifying r = -0.008327554Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.008327554, -0.008327554}
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