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Simplifying -16r2 + 28r + 575 = 0 Reorder the terms: 575 + 28r + -16r2 = 0 Solving 575 + 28r + -16r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -35.9375 + -1.75r + r2 = 0 Move the constant term to the right: Add '35.9375' to each side of the equation. -35.9375 + -1.75r + 35.9375 + r2 = 0 + 35.9375 Reorder the terms: -35.9375 + 35.9375 + -1.75r + r2 = 0 + 35.9375 Combine like terms: -35.9375 + 35.9375 = 0.0000 0.0000 + -1.75r + r2 = 0 + 35.9375 -1.75r + r2 = 0 + 35.9375 Combine like terms: 0 + 35.9375 = 35.9375 -1.75r + r2 = 35.9375 The r term is -1.75r. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75r + 0.765625 + r2 = 35.9375 + 0.765625 Reorder the terms: 0.765625 + -1.75r + r2 = 35.9375 + 0.765625 Combine like terms: 35.9375 + 0.765625 = 36.703125 0.765625 + -1.75r + r2 = 36.703125 Factor a perfect square on the left side: (r + -0.875)(r + -0.875) = 36.703125 Calculate the square root of the right side: 6.058310408 Break this problem into two subproblems by setting (r + -0.875) equal to 6.058310408 and -6.058310408.Subproblem 1
r + -0.875 = 6.058310408 Simplifying r + -0.875 = 6.058310408 Reorder the terms: -0.875 + r = 6.058310408 Solving -0.875 + r = 6.058310408 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + r = 6.058310408 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + r = 6.058310408 + 0.875 r = 6.058310408 + 0.875 Combine like terms: 6.058310408 + 0.875 = 6.933310408 r = 6.933310408 Simplifying r = 6.933310408Subproblem 2
r + -0.875 = -6.058310408 Simplifying r + -0.875 = -6.058310408 Reorder the terms: -0.875 + r = -6.058310408 Solving -0.875 + r = -6.058310408 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + r = -6.058310408 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + r = -6.058310408 + 0.875 r = -6.058310408 + 0.875 Combine like terms: -6.058310408 + 0.875 = -5.183310408 r = -5.183310408 Simplifying r = -5.183310408Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.933310408, -5.183310408}
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