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Simplifying 10r2 + 7r + -16 = 0 Reorder the terms: -16 + 7r + 10r2 = 0 Solving -16 + 7r + 10r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.6 + 0.7r + r2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 0.7r + 1.6 + r2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 0.7r + r2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 0.7r + r2 = 0 + 1.6 0.7r + r2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 0.7r + r2 = 1.6 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 = 1.6 + 0.1225 Reorder the terms: 0.1225 + 0.7r + r2 = 1.6 + 0.1225 Combine like terms: 1.6 + 0.1225 = 1.7225 0.1225 + 0.7r + r2 = 1.7225 Factor a perfect square on the left side: (r + 0.35)(r + 0.35) = 1.7225 Calculate the square root of the right side: 1.312440475 Break this problem into two subproblems by setting (r + 0.35) equal to 1.312440475 and -1.312440475.Subproblem 1
r + 0.35 = 1.312440475 Simplifying r + 0.35 = 1.312440475 Reorder the terms: 0.35 + r = 1.312440475 Solving 0.35 + r = 1.312440475 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 = 1.312440475 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + r = 1.312440475 + -0.35 r = 1.312440475 + -0.35 Combine like terms: 1.312440475 + -0.35 = 0.962440475 r = 0.962440475 Simplifying r = 0.962440475Subproblem 2
r + 0.35 = -1.312440475 Simplifying r + 0.35 = -1.312440475 Reorder the terms: 0.35 + r = -1.312440475 Solving 0.35 + r = -1.312440475 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 = -1.312440475 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + r = -1.312440475 + -0.35 r = -1.312440475 + -0.35 Combine like terms: -1.312440475 + -0.35 = -1.662440475 r = -1.662440475 Simplifying r = -1.662440475Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.962440475, -1.662440475}
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