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Simplifying -4r2 + 64r + -76 = 0 Reorder the terms: -76 + 64r + -4r2 = 0 Solving -76 + 64r + -4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(-19 + 16r + -1r2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-19 + 16r + -1r2)' equal to zero and attempt to solve: Simplifying -19 + 16r + -1r2 = 0 Solving -19 + 16r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 19 + -16r + r2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + -16r + -19 + r2 = 0 + -19 Reorder the terms: 19 + -19 + -16r + r2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -16r + r2 = 0 + -19 -16r + r2 = 0 + -19 Combine like terms: 0 + -19 = -19 -16r + r2 = -19 The r term is -16r. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16r + 64 + r2 = -19 + 64 Reorder the terms: 64 + -16r + r2 = -19 + 64 Combine like terms: -19 + 64 = 45 64 + -16r + r2 = 45 Factor a perfect square on the left side: (r + -8)(r + -8) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (r + -8) equal to 6.708203933 and -6.708203933.Subproblem 1
r + -8 = 6.708203933 Simplifying r + -8 = 6.708203933 Reorder the terms: -8 + r = 6.708203933 Solving -8 + r = 6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = 6.708203933 + 8 Combine like terms: -8 + 8 = 0 0 + r = 6.708203933 + 8 r = 6.708203933 + 8 Combine like terms: 6.708203933 + 8 = 14.708203933 r = 14.708203933 Simplifying r = 14.708203933Subproblem 2
r + -8 = -6.708203933 Simplifying r + -8 = -6.708203933 Reorder the terms: -8 + r = -6.708203933 Solving -8 + r = -6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = -6.708203933 + 8 Combine like terms: -8 + 8 = 0 0 + r = -6.708203933 + 8 r = -6.708203933 + 8 Combine like terms: -6.708203933 + 8 = 1.291796067 r = 1.291796067 Simplifying r = 1.291796067Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.708203933, 1.291796067}Solution
r = {14.708203933, 1.291796067}
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