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Simplifying 9r2 + -5r + -56 = 0 Reorder the terms: -56 + -5r + 9r2 = 0 Solving -56 + -5r + 9r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.222222222 + -0.5555555556r + r2 = 0 Move the constant term to the right: Add '6.222222222' to each side of the equation. -6.222222222 + -0.5555555556r + 6.222222222 + r2 = 0 + 6.222222222 Reorder the terms: -6.222222222 + 6.222222222 + -0.5555555556r + r2 = 0 + 6.222222222 Combine like terms: -6.222222222 + 6.222222222 = 0.000000000 0.000000000 + -0.5555555556r + r2 = 0 + 6.222222222 -0.5555555556r + r2 = 0 + 6.222222222 Combine like terms: 0 + 6.222222222 = 6.222222222 -0.5555555556r + r2 = 6.222222222 The r term is -0.5555555556r. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556r + 0.07716049384 + r2 = 6.222222222 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556r + r2 = 6.222222222 + 0.07716049384 Combine like terms: 6.222222222 + 0.07716049384 = 6.29938271584 0.07716049384 + -0.5555555556r + r2 = 6.29938271584 Factor a perfect square on the left side: (r + -0.2777777778)(r + -0.2777777778) = 6.29938271584 Calculate the square root of the right side: 2.509857111 Break this problem into two subproblems by setting (r + -0.2777777778) equal to 2.509857111 and -2.509857111.Subproblem 1
r + -0.2777777778 = 2.509857111 Simplifying r + -0.2777777778 = 2.509857111 Reorder the terms: -0.2777777778 + r = 2.509857111 Solving -0.2777777778 + r = 2.509857111 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + r = 2.509857111 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + r = 2.509857111 + 0.2777777778 r = 2.509857111 + 0.2777777778 Combine like terms: 2.509857111 + 0.2777777778 = 2.7876348888 r = 2.7876348888 Simplifying r = 2.7876348888Subproblem 2
r + -0.2777777778 = -2.509857111 Simplifying r + -0.2777777778 = -2.509857111 Reorder the terms: -0.2777777778 + r = -2.509857111 Solving -0.2777777778 + r = -2.509857111 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + r = -2.509857111 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + r = -2.509857111 + 0.2777777778 r = -2.509857111 + 0.2777777778 Combine like terms: -2.509857111 + 0.2777777778 = -2.2320793332 r = -2.2320793332 Simplifying r = -2.2320793332Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.7876348888, -2.2320793332}
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