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Simplifying x2 + -117x + 2196 = 0 Reorder the terms: 2196 + -117x + x2 = 0 Solving 2196 + -117x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2196' to each side of the equation. 2196 + -117x + -2196 + x2 = 0 + -2196 Reorder the terms: 2196 + -2196 + -117x + x2 = 0 + -2196 Combine like terms: 2196 + -2196 = 0 0 + -117x + x2 = 0 + -2196 -117x + x2 = 0 + -2196 Combine like terms: 0 + -2196 = -2196 -117x + x2 = -2196 The x term is -117x. Take half its coefficient (-58.5). Square it (3422.25) and add it to both sides. Add '3422.25' to each side of the equation. -117x + 3422.25 + x2 = -2196 + 3422.25 Reorder the terms: 3422.25 + -117x + x2 = -2196 + 3422.25 Combine like terms: -2196 + 3422.25 = 1226.25 3422.25 + -117x + x2 = 1226.25 Factor a perfect square on the left side: (x + -58.5)(x + -58.5) = 1226.25 Calculate the square root of the right side: 35.01785259 Break this problem into two subproblems by setting (x + -58.5) equal to 35.01785259 and -35.01785259.Subproblem 1
x + -58.5 = 35.01785259 Simplifying x + -58.5 = 35.01785259 Reorder the terms: -58.5 + x = 35.01785259 Solving -58.5 + x = 35.01785259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.5' to each side of the equation. -58.5 + 58.5 + x = 35.01785259 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + x = 35.01785259 + 58.5 x = 35.01785259 + 58.5 Combine like terms: 35.01785259 + 58.5 = 93.51785259 x = 93.51785259 Simplifying x = 93.51785259Subproblem 2
x + -58.5 = -35.01785259 Simplifying x + -58.5 = -35.01785259 Reorder the terms: -58.5 + x = -35.01785259 Solving -58.5 + x = -35.01785259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.5' to each side of the equation. -58.5 + 58.5 + x = -35.01785259 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + x = -35.01785259 + 58.5 x = -35.01785259 + 58.5 Combine like terms: -35.01785259 + 58.5 = 23.48214741 x = 23.48214741 Simplifying x = 23.48214741Solution
The solution to the problem is based on the solutions from the subproblems. x = {93.51785259, 23.48214741}
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