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Simplifying -4r2 + 18 = -2r Reorder the terms: 18 + -4r2 = -2r Solving 18 + -4r2 = -2r Solving for variable 'r'. Reorder the terms: 18 + 2r + -4r2 = -2r + 2r Combine like terms: -2r + 2r = 0 18 + 2r + -4r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + r + -2r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + r + -2r2)' equal to zero and attempt to solve: Simplifying 9 + r + -2r2 = 0 Solving 9 + r + -2r2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -0.5r + r2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -0.5r + 4.5 + r2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -0.5r + r2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -0.5r + r2 = 0 + 4.5 -0.5r + r2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -0.5r + r2 = 4.5 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5r + 0.25 + r2 = 4.5 + 0.25 Reorder the terms: 0.25 + -0.5r + r2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + -0.5r + r2 = 4.75 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (r + 0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
r + 0.5 = 2.179449472 Simplifying r + 0.5 = 2.179449472 Reorder the terms: 0.5 + r = 2.179449472 Solving 0.5 + r = 2.179449472 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 2.179449472 + -0.5 r = 2.179449472 + -0.5 Combine like terms: 2.179449472 + -0.5 = 1.679449472 r = 1.679449472 Simplifying r = 1.679449472Subproblem 2
r + 0.5 = -2.179449472 Simplifying r + 0.5 = -2.179449472 Reorder the terms: 0.5 + r = -2.179449472 Solving 0.5 + r = -2.179449472 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -2.179449472 + -0.5 r = -2.179449472 + -0.5 Combine like terms: -2.179449472 + -0.5 = -2.679449472 r = -2.679449472 Simplifying r = -2.679449472Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.679449472, -2.679449472}Solution
r = {1.679449472, -2.679449472}
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