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Simplifying 10r2 = 15 + -7r Solving 10r2 = 15 + -7r Solving for variable 'r'. Reorder the terms: -15 + 7r + 10r2 = 15 + -7r + -15 + 7r Reorder the terms: -15 + 7r + 10r2 = 15 + -15 + -7r + 7r Combine like terms: 15 + -15 = 0 -15 + 7r + 10r2 = 0 + -7r + 7r -15 + 7r + 10r2 = -7r + 7r Combine like terms: -7r + 7r = 0 -15 + 7r + 10r2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + 0.7r + r2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.7r + 1.5 + r2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.7r + r2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.7r + r2 = 0 + 1.5 0.7r + r2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.7r + r2 = 1.5 The r term is 0.7r. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7r + 0.1225 + r2 = 1.5 + 0.1225 Reorder the terms: 0.1225 + 0.7r + r2 = 1.5 + 0.1225 Combine like terms: 1.5 + 0.1225 = 1.6225 0.1225 + 0.7r + r2 = 1.6225 Factor a perfect square on the left side: (r + 0.35)(r + 0.35) = 1.6225 Calculate the square root of the right side: 1.27377392 Break this problem into two subproblems by setting (r + 0.35) equal to 1.27377392 and -1.27377392.Subproblem 1
r + 0.35 = 1.27377392 Simplifying r + 0.35 = 1.27377392 Reorder the terms: 0.35 + r = 1.27377392 Solving 0.35 + r = 1.27377392 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + r = 1.27377392 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + r = 1.27377392 + -0.35 r = 1.27377392 + -0.35 Combine like terms: 1.27377392 + -0.35 = 0.92377392 r = 0.92377392 Simplifying r = 0.92377392Subproblem 2
r + 0.35 = -1.27377392 Simplifying r + 0.35 = -1.27377392 Reorder the terms: 0.35 + r = -1.27377392 Solving 0.35 + r = -1.27377392 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + r = -1.27377392 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + r = -1.27377392 + -0.35 r = -1.27377392 + -0.35 Combine like terms: -1.27377392 + -0.35 = -1.62377392 r = -1.62377392 Simplifying r = -1.62377392Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.92377392, -1.62377392}
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