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Simplifying 14 = 0.01125x2 + 0.1825x + 1.75 Reorder the terms: 14 = 1.75 + 0.1825x + 0.01125x2 Solving 14 = 1.75 + 0.1825x + 0.01125x2 Solving for variable 'x'. Combine like terms: 14 + -1.75 = 12.25 12.25 + -0.1825x + -0.01125x2 = 1.75 + 0.1825x + 0.01125x2 + -1.75 + -0.1825x + -0.01125x2 Reorder the terms: 12.25 + -0.1825x + -0.01125x2 = 1.75 + -1.75 + 0.1825x + -0.1825x + 0.01125x2 + -0.01125x2 Combine like terms: 1.75 + -1.75 = 0.00 12.25 + -0.1825x + -0.01125x2 = 0.00 + 0.1825x + -0.1825x + 0.01125x2 + -0.01125x2 12.25 + -0.1825x + -0.01125x2 = 0.1825x + -0.1825x + 0.01125x2 + -0.01125x2 Combine like terms: 0.1825x + -0.1825x = 0.0000 12.25 + -0.1825x + -0.01125x2 = 0.0000 + 0.01125x2 + -0.01125x2 12.25 + -0.1825x + -0.01125x2 = 0.01125x2 + -0.01125x2 Combine like terms: 0.01125x2 + -0.01125x2 = 0.00000 12.25 + -0.1825x + -0.01125x2 = 0.00000 Begin completing the square. Divide all terms by -0.01125 the coefficient of the squared term: Divide each side by '-0.01125'. -1088.888889 + 16.22222222x + x2 = 0 Move the constant term to the right: Add '1088.888889' to each side of the equation. -1088.888889 + 16.22222222x + 1088.888889 + x2 = 0 + 1088.888889 Reorder the terms: -1088.888889 + 1088.888889 + 16.22222222x + x2 = 0 + 1088.888889 Combine like terms: -1088.888889 + 1088.888889 = 0.000000 0.000000 + 16.22222222x + x2 = 0 + 1088.888889 16.22222222x + x2 = 0 + 1088.888889 Combine like terms: 0 + 1088.888889 = 1088.888889 16.22222222x + x2 = 1088.888889 The x term is 16.22222222x. Take half its coefficient (8.11111111). Square it (65.79012344) and add it to both sides. Add '65.79012344' to each side of the equation. 16.22222222x + 65.79012344 + x2 = 1088.888889 + 65.79012344 Reorder the terms: 65.79012344 + 16.22222222x + x2 = 1088.888889 + 65.79012344 Combine like terms: 1088.888889 + 65.79012344 = 1154.67901244 65.79012344 + 16.22222222x + x2 = 1154.67901244 Factor a perfect square on the left side: (x + 8.11111111)(x + 8.11111111) = 1154.67901244 Calculate the square root of the right side: 33.980568159 Break this problem into two subproblems by setting (x + 8.11111111) equal to 33.980568159 and -33.980568159.Subproblem 1
x + 8.11111111 = 33.980568159 Simplifying x + 8.11111111 = 33.980568159 Reorder the terms: 8.11111111 + x = 33.980568159 Solving 8.11111111 + x = 33.980568159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.11111111' to each side of the equation. 8.11111111 + -8.11111111 + x = 33.980568159 + -8.11111111 Combine like terms: 8.11111111 + -8.11111111 = 0.00000000 0.00000000 + x = 33.980568159 + -8.11111111 x = 33.980568159 + -8.11111111 Combine like terms: 33.980568159 + -8.11111111 = 25.869457049 x = 25.869457049 Simplifying x = 25.869457049Subproblem 2
x + 8.11111111 = -33.980568159 Simplifying x + 8.11111111 = -33.980568159 Reorder the terms: 8.11111111 + x = -33.980568159 Solving 8.11111111 + x = -33.980568159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.11111111' to each side of the equation. 8.11111111 + -8.11111111 + x = -33.980568159 + -8.11111111 Combine like terms: 8.11111111 + -8.11111111 = 0.00000000 0.00000000 + x = -33.980568159 + -8.11111111 x = -33.980568159 + -8.11111111 Combine like terms: -33.980568159 + -8.11111111 = -42.091679269 x = -42.091679269 Simplifying x = -42.091679269Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.869457049, -42.091679269}
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