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Simplifying (2x + -5) * x = 186 Reorder the terms: (-5 + 2x) * x = 186 Reorder the terms for easier multiplication: x(-5 + 2x) = 186 (-5 * x + 2x * x) = 186 (-5x + 2x2) = 186 Solving -5x + 2x2 = 186 Solving for variable 'x'. Reorder the terms: -186 + -5x + 2x2 = 186 + -186 Combine like terms: 186 + -186 = 0 -186 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -93 + -2.5x + x2 = 0 Move the constant term to the right: Add '93' to each side of the equation. -93 + -2.5x + 93 + x2 = 0 + 93 Reorder the terms: -93 + 93 + -2.5x + x2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + -2.5x + x2 = 0 + 93 -2.5x + x2 = 0 + 93 Combine like terms: 0 + 93 = 93 -2.5x + x2 = 93 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 93 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 93 + 1.5625 Combine like terms: 93 + 1.5625 = 94.5625 1.5625 + -2.5x + x2 = 94.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 94.5625 Calculate the square root of the right side: 9.724325169 Break this problem into two subproblems by setting (x + -1.25) equal to 9.724325169 and -9.724325169.Subproblem 1
x + -1.25 = 9.724325169 Simplifying x + -1.25 = 9.724325169 Reorder the terms: -1.25 + x = 9.724325169 Solving -1.25 + x = 9.724325169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 9.724325169 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 9.724325169 + 1.25 x = 9.724325169 + 1.25 Combine like terms: 9.724325169 + 1.25 = 10.974325169 x = 10.974325169 Simplifying x = 10.974325169Subproblem 2
x + -1.25 = -9.724325169 Simplifying x + -1.25 = -9.724325169 Reorder the terms: -1.25 + x = -9.724325169 Solving -1.25 + x = -9.724325169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -9.724325169 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -9.724325169 + 1.25 x = -9.724325169 + 1.25 Combine like terms: -9.724325169 + 1.25 = -8.474325169 x = -8.474325169 Simplifying x = -8.474325169Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.974325169, -8.474325169}
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