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Simplifying 7r2 + 37r + -3 = 0 Reorder the terms: -3 + 37r + 7r2 = 0 Solving -3 + 37r + 7r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 5.285714286r + r2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 5.285714286r + 0.4285714286 + r2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 5.285714286r + r2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 5.285714286r + r2 = 0 + 0.4285714286 5.285714286r + r2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 5.285714286r + r2 = 0.4285714286 The r term is 5.285714286r. Take half its coefficient (2.642857143). Square it (6.984693878) and add it to both sides. Add '6.984693878' to each side of the equation. 5.285714286r + 6.984693878 + r2 = 0.4285714286 + 6.984693878 Reorder the terms: 6.984693878 + 5.285714286r + r2 = 0.4285714286 + 6.984693878 Combine like terms: 0.4285714286 + 6.984693878 = 7.4132653066 6.984693878 + 5.285714286r + r2 = 7.4132653066 Factor a perfect square on the left side: (r + 2.642857143)(r + 2.642857143) = 7.4132653066 Calculate the square root of the right side: 2.722731222 Break this problem into two subproblems by setting (r + 2.642857143) equal to 2.722731222 and -2.722731222.Subproblem 1
r + 2.642857143 = 2.722731222 Simplifying r + 2.642857143 = 2.722731222 Reorder the terms: 2.642857143 + r = 2.722731222 Solving 2.642857143 + r = 2.722731222 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.642857143' to each side of the equation. 2.642857143 + -2.642857143 + r = 2.722731222 + -2.642857143 Combine like terms: 2.642857143 + -2.642857143 = 0.000000000 0.000000000 + r = 2.722731222 + -2.642857143 r = 2.722731222 + -2.642857143 Combine like terms: 2.722731222 + -2.642857143 = 0.079874079 r = 0.079874079 Simplifying r = 0.079874079Subproblem 2
r + 2.642857143 = -2.722731222 Simplifying r + 2.642857143 = -2.722731222 Reorder the terms: 2.642857143 + r = -2.722731222 Solving 2.642857143 + r = -2.722731222 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.642857143' to each side of the equation. 2.642857143 + -2.642857143 + r = -2.722731222 + -2.642857143 Combine like terms: 2.642857143 + -2.642857143 = 0.000000000 0.000000000 + r = -2.722731222 + -2.642857143 r = -2.722731222 + -2.642857143 Combine like terms: -2.722731222 + -2.642857143 = -5.365588365 r = -5.365588365 Simplifying r = -5.365588365Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.079874079, -5.365588365}
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