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Simplifying 4r2 + 6r + -5 = 0 Reorder the terms: -5 + 6r + 4r2 = 0 Solving -5 + 6r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 1.5r + r2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.5r + 1.25 + r2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.5r + r2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.5r + r2 = 0 + 1.25 1.5r + r2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.5r + r2 = 1.25 The r term is 1.5r. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5r + 0.5625 + r2 = 1.25 + 0.5625 Reorder the terms: 0.5625 + 1.5r + r2 = 1.25 + 0.5625 Combine like terms: 1.25 + 0.5625 = 1.8125 0.5625 + 1.5r + r2 = 1.8125 Factor a perfect square on the left side: (r + 0.75)(r + 0.75) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (r + 0.75) equal to 1.346291202 and -1.346291202.Subproblem 1
r + 0.75 = 1.346291202 Simplifying r + 0.75 = 1.346291202 Reorder the terms: 0.75 + r = 1.346291202 Solving 0.75 + r = 1.346291202 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + r = 1.346291202 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + r = 1.346291202 + -0.75 r = 1.346291202 + -0.75 Combine like terms: 1.346291202 + -0.75 = 0.596291202 r = 0.596291202 Simplifying r = 0.596291202Subproblem 2
r + 0.75 = -1.346291202 Simplifying r + 0.75 = -1.346291202 Reorder the terms: 0.75 + r = -1.346291202 Solving 0.75 + r = -1.346291202 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + r = -1.346291202 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + r = -1.346291202 + -0.75 r = -1.346291202 + -0.75 Combine like terms: -1.346291202 + -0.75 = -2.096291202 r = -2.096291202 Simplifying r = -2.096291202Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.596291202, -2.096291202}
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