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Simplifying 4r2 + -18r + -100 = 0 Reorder the terms: -100 + -18r + 4r2 = 0 Solving -100 + -18r + 4r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -9r + 2r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + -9r + 2r2)' equal to zero and attempt to solve: Simplifying -50 + -9r + 2r2 = 0 Solving -50 + -9r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + -4.5r + r2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -4.5r + 25 + r2 = 0 + 25 Reorder the terms: -25 + 25 + -4.5r + r2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4.5r + r2 = 0 + 25 -4.5r + r2 = 0 + 25 Combine like terms: 0 + 25 = 25 -4.5r + r2 = 25 The r term is -4.5r. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5r + 5.0625 + r2 = 25 + 5.0625 Reorder the terms: 5.0625 + -4.5r + r2 = 25 + 5.0625 Combine like terms: 25 + 5.0625 = 30.0625 5.0625 + -4.5r + r2 = 30.0625 Factor a perfect square on the left side: (r + -2.25)(r + -2.25) = 30.0625 Calculate the square root of the right side: 5.48292805 Break this problem into two subproblems by setting (r + -2.25) equal to 5.48292805 and -5.48292805.Subproblem 1
r + -2.25 = 5.48292805 Simplifying r + -2.25 = 5.48292805 Reorder the terms: -2.25 + r = 5.48292805 Solving -2.25 + r = 5.48292805 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + r = 5.48292805 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + r = 5.48292805 + 2.25 r = 5.48292805 + 2.25 Combine like terms: 5.48292805 + 2.25 = 7.73292805 r = 7.73292805 Simplifying r = 7.73292805Subproblem 2
r + -2.25 = -5.48292805 Simplifying r + -2.25 = -5.48292805 Reorder the terms: -2.25 + r = -5.48292805 Solving -2.25 + r = -5.48292805 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + r = -5.48292805 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + r = -5.48292805 + 2.25 r = -5.48292805 + 2.25 Combine like terms: -5.48292805 + 2.25 = -3.23292805 r = -3.23292805 Simplifying r = -3.23292805Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.73292805, -3.23292805}Solution
r = {7.73292805, -3.23292805}
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