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Simplifying -2r2 + -10r = -56 Reorder the terms: -10r + -2r2 = -56 Solving -10r + -2r2 = -56 Solving for variable 'r'. Reorder the terms: 56 + -10r + -2r2 = -56 + 56 Combine like terms: -56 + 56 = 0 56 + -10r + -2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(28 + -5r + -1r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(28 + -5r + -1r2)' equal to zero and attempt to solve: Simplifying 28 + -5r + -1r2 = 0 Solving 28 + -5r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + 5r + r2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 5r + 28 + r2 = 0 + 28 Reorder the terms: -28 + 28 + 5r + r2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 5r + r2 = 0 + 28 5r + r2 = 0 + 28 Combine like terms: 0 + 28 = 28 5r + r2 = 28 The r term is 5r. 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. 5r + 6.25 + r2 = 28 + 6.25 Reorder the terms: 6.25 + 5r + r2 = 28 + 6.25 Combine like terms: 28 + 6.25 = 34.25 6.25 + 5r + r2 = 34.25 Factor a perfect square on the left side: (r + 2.5)(r + 2.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (r + 2.5) equal to 5.852349955 and -5.852349955.Subproblem 1
r + 2.5 = 5.852349955 Simplifying r + 2.5 = 5.852349955 Reorder the terms: 2.5 + r = 5.852349955 Solving 2.5 + r = 5.852349955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = 5.852349955 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 5.852349955 + -2.5 r = 5.852349955 + -2.5 Combine like terms: 5.852349955 + -2.5 = 3.352349955 r = 3.352349955 Simplifying r = 3.352349955Subproblem 2
r + 2.5 = -5.852349955 Simplifying r + 2.5 = -5.852349955 Reorder the terms: 2.5 + r = -5.852349955 Solving 2.5 + r = -5.852349955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = -5.852349955 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -5.852349955 + -2.5 r = -5.852349955 + -2.5 Combine like terms: -5.852349955 + -2.5 = -8.352349955 r = -8.352349955 Simplifying r = -8.352349955Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.352349955, -8.352349955}Solution
r = {3.352349955, -8.352349955}
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