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Simplifying 35r2 + -69r + -70 = 0 Reorder the terms: -70 + -69r + 35r2 = 0 Solving -70 + -69r + 35r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -2 + -1.971428571r + r2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.971428571r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + -1.971428571r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.971428571r + r2 = 0 + 2 -1.971428571r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.971428571r + r2 = 2 The r term is -1.971428571r. Take half its coefficient (-0.9857142855). Square it (0.9716326526) and add it to both sides. Add '0.9716326526' to each side of the equation. -1.971428571r + 0.9716326526 + r2 = 2 + 0.9716326526 Reorder the terms: 0.9716326526 + -1.971428571r + r2 = 2 + 0.9716326526 Combine like terms: 2 + 0.9716326526 = 2.9716326526 0.9716326526 + -1.971428571r + r2 = 2.9716326526 Factor a perfect square on the left side: (r + -0.9857142855)(r + -0.9857142855) = 2.9716326526 Calculate the square root of the right side: 1.723842409 Break this problem into two subproblems by setting (r + -0.9857142855) equal to 1.723842409 and -1.723842409.Subproblem 1
r + -0.9857142855 = 1.723842409 Simplifying r + -0.9857142855 = 1.723842409 Reorder the terms: -0.9857142855 + r = 1.723842409 Solving -0.9857142855 + r = 1.723842409 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.9857142855' to each side of the equation. -0.9857142855 + 0.9857142855 + r = 1.723842409 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + r = 1.723842409 + 0.9857142855 r = 1.723842409 + 0.9857142855 Combine like terms: 1.723842409 + 0.9857142855 = 2.7095566945 r = 2.7095566945 Simplifying r = 2.7095566945Subproblem 2
r + -0.9857142855 = -1.723842409 Simplifying r + -0.9857142855 = -1.723842409 Reorder the terms: -0.9857142855 + r = -1.723842409 Solving -0.9857142855 + r = -1.723842409 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.9857142855' to each side of the equation. -0.9857142855 + 0.9857142855 + r = -1.723842409 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + r = -1.723842409 + 0.9857142855 r = -1.723842409 + 0.9857142855 Combine like terms: -1.723842409 + 0.9857142855 = -0.7381281235 r = -0.7381281235 Simplifying r = -0.7381281235Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.7095566945, -0.7381281235}
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