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Simplifying 4r2 + -15r + 7 = 0 Reorder the terms: 7 + -15r + 4r2 = 0 Solving 7 + -15r + 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'. 1.75 + -3.75r + r2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -3.75r + -1.75 + r2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -3.75r + r2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -3.75r + r2 = 0 + -1.75 -3.75r + r2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -3.75r + r2 = -1.75 The r term is -3.75r. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75r + 3.515625 + r2 = -1.75 + 3.515625 Reorder the terms: 3.515625 + -3.75r + r2 = -1.75 + 3.515625 Combine like terms: -1.75 + 3.515625 = 1.765625 3.515625 + -3.75r + r2 = 1.765625 Factor a perfect square on the left side: (r + -1.875)(r + -1.875) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (r + -1.875) equal to 1.328768227 and -1.328768227.Subproblem 1
r + -1.875 = 1.328768227 Simplifying r + -1.875 = 1.328768227 Reorder the terms: -1.875 + r = 1.328768227 Solving -1.875 + r = 1.328768227 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + r = 1.328768227 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + r = 1.328768227 + 1.875 r = 1.328768227 + 1.875 Combine like terms: 1.328768227 + 1.875 = 3.203768227 r = 3.203768227 Simplifying r = 3.203768227Subproblem 2
r + -1.875 = -1.328768227 Simplifying r + -1.875 = -1.328768227 Reorder the terms: -1.875 + r = -1.328768227 Solving -1.875 + r = -1.328768227 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + r = -1.328768227 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + r = -1.328768227 + 1.875 r = -1.328768227 + 1.875 Combine like terms: -1.328768227 + 1.875 = 0.546231773 r = 0.546231773 Simplifying r = 0.546231773Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.203768227, 0.546231773}
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