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Simplifying 4r2 + -7r + -10 = 0 Reorder the terms: -10 + -7r + 4r2 = 0 Solving -10 + -7r + 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'. -2.5 + -1.75r + r2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1.75r + 2.5 + r2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1.75r + r2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1.75r + r2 = 0 + 2.5 -1.75r + r2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1.75r + r2 = 2.5 The r term is -1.75r. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75r + 0.765625 + r2 = 2.5 + 0.765625 Reorder the terms: 0.765625 + -1.75r + r2 = 2.5 + 0.765625 Combine like terms: 2.5 + 0.765625 = 3.265625 0.765625 + -1.75r + r2 = 3.265625 Factor a perfect square on the left side: (r + -0.875)(r + -0.875) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (r + -0.875) equal to 1.807104037 and -1.807104037.Subproblem 1
r + -0.875 = 1.807104037 Simplifying r + -0.875 = 1.807104037 Reorder the terms: -0.875 + r = 1.807104037 Solving -0.875 + r = 1.807104037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + r = 1.807104037 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + r = 1.807104037 + 0.875 r = 1.807104037 + 0.875 Combine like terms: 1.807104037 + 0.875 = 2.682104037 r = 2.682104037 Simplifying r = 2.682104037Subproblem 2
r + -0.875 = -1.807104037 Simplifying r + -0.875 = -1.807104037 Reorder the terms: -0.875 + r = -1.807104037 Solving -0.875 + r = -1.807104037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + r = -1.807104037 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + r = -1.807104037 + 0.875 r = -1.807104037 + 0.875 Combine like terms: -1.807104037 + 0.875 = -0.932104037 r = -0.932104037 Simplifying r = -0.932104037Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.682104037, -0.932104037}
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