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Simplifying 10r2 + 7r + -4 = 0 Reorder the terms: -4 + 7r + 10r2 = 0 Solving -4 + 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'. -0.4 + 0.7r + r2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.7r + 0.4 + r2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.7r + r2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.7r + r2 = 0 + 0.4 0.7r + r2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.7r + r2 = 0.4 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 = 0.4 + 0.1225 Reorder the terms: 0.1225 + 0.7r + r2 = 0.4 + 0.1225 Combine like terms: 0.4 + 0.1225 = 0.5225 0.1225 + 0.7r + r2 = 0.5225 Factor a perfect square on the left side: (r + 0.35)(r + 0.35) = 0.5225 Calculate the square root of the right side: 0.722841615 Break this problem into two subproblems by setting (r + 0.35) equal to 0.722841615 and -0.722841615.Subproblem 1
r + 0.35 = 0.722841615 Simplifying r + 0.35 = 0.722841615 Reorder the terms: 0.35 + r = 0.722841615 Solving 0.35 + r = 0.722841615 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 = 0.722841615 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + r = 0.722841615 + -0.35 r = 0.722841615 + -0.35 Combine like terms: 0.722841615 + -0.35 = 0.372841615 r = 0.372841615 Simplifying r = 0.372841615Subproblem 2
r + 0.35 = -0.722841615 Simplifying r + 0.35 = -0.722841615 Reorder the terms: 0.35 + r = -0.722841615 Solving 0.35 + r = -0.722841615 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 = -0.722841615 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + r = -0.722841615 + -0.35 r = -0.722841615 + -0.35 Combine like terms: -0.722841615 + -0.35 = -1.072841615 r = -1.072841615 Simplifying r = -1.072841615Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.372841615, -1.072841615}
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