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Simplifying x2 + -24x = -25.75 Reorder the terms: -24x + x2 = -25.75 Solving -24x + x2 = -25.75 Solving for variable 'x'. Reorder the terms: 25.75 + -24x + x2 = -25.75 + 25.75 Combine like terms: -25.75 + 25.75 = 0.00 25.75 + -24x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-25.75' to each side of the equation. 25.75 + -24x + -25.75 + x2 = 0.00 + -25.75 Reorder the terms: 25.75 + -25.75 + -24x + x2 = 0.00 + -25.75 Combine like terms: 25.75 + -25.75 = 0.00 0.00 + -24x + x2 = 0.00 + -25.75 -24x + x2 = 0.00 + -25.75 Combine like terms: 0.00 + -25.75 = -25.75 -24x + x2 = -25.75 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -25.75 + 144 Reorder the terms: 144 + -24x + x2 = -25.75 + 144 Combine like terms: -25.75 + 144 = 118.25 144 + -24x + x2 = 118.25 Factor a perfect square on the left side: (x + -12)(x + -12) = 118.25 Calculate the square root of the right side: 10.874281585 Break this problem into two subproblems by setting (x + -12) equal to 10.874281585 and -10.874281585.Subproblem 1
x + -12 = 10.874281585 Simplifying x + -12 = 10.874281585 Reorder the terms: -12 + x = 10.874281585 Solving -12 + x = 10.874281585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 10.874281585 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10.874281585 + 12 x = 10.874281585 + 12 Combine like terms: 10.874281585 + 12 = 22.874281585 x = 22.874281585 Simplifying x = 22.874281585Subproblem 2
x + -12 = -10.874281585 Simplifying x + -12 = -10.874281585 Reorder the terms: -12 + x = -10.874281585 Solving -12 + x = -10.874281585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -10.874281585 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10.874281585 + 12 x = -10.874281585 + 12 Combine like terms: -10.874281585 + 12 = 1.125718415 x = 1.125718415 Simplifying x = 1.125718415Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.874281585, 1.125718415}
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