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Simplifying 4r2 + 16r + -10 = 0 Reorder the terms: -10 + 16r + 4r2 = 0 Solving -10 + 16r + 4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 8r + 2r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 8r + 2r2)' equal to zero and attempt to solve: Simplifying -5 + 8r + 2r2 = 0 Solving -5 + 8r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 4r + r2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 4r + 2.5 + r2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 4r + r2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 4r + r2 = 0 + 2.5 4r + r2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 4r + r2 = 2.5 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 2.5 + 4 Reorder the terms: 4 + 4r + r2 = 2.5 + 4 Combine like terms: 2.5 + 4 = 6.5 4 + 4r + r2 = 6.5 Factor a perfect square on the left side: (r + 2)(r + 2) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (r + 2) equal to 2.549509757 and -2.549509757.Subproblem 1
r + 2 = 2.549509757 Simplifying r + 2 = 2.549509757 Reorder the terms: 2 + r = 2.549509757 Solving 2 + r = 2.549509757 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 2.549509757 + -2 Combine like terms: 2 + -2 = 0 0 + r = 2.549509757 + -2 r = 2.549509757 + -2 Combine like terms: 2.549509757 + -2 = 0.549509757 r = 0.549509757 Simplifying r = 0.549509757Subproblem 2
r + 2 = -2.549509757 Simplifying r + 2 = -2.549509757 Reorder the terms: 2 + r = -2.549509757 Solving 2 + r = -2.549509757 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -2.549509757 + -2 Combine like terms: 2 + -2 = 0 0 + r = -2.549509757 + -2 r = -2.549509757 + -2 Combine like terms: -2.549509757 + -2 = -4.549509757 r = -4.549509757 Simplifying r = -4.549509757Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.549509757, -4.549509757}Solution
r = {0.549509757, -4.549509757}
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