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Simplifying x2 + -24x + -160 = 0 Reorder the terms: -160 + -24x + x2 = 0 Solving -160 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -24x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -24x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -24x + x2 = 0 + 160 -24x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -24x + x2 = 160 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 = 160 + 144 Reorder the terms: 144 + -24x + x2 = 160 + 144 Combine like terms: 160 + 144 = 304 144 + -24x + x2 = 304 Factor a perfect square on the left side: (x + -12)(x + -12) = 304 Calculate the square root of the right side: 17.435595774 Break this problem into two subproblems by setting (x + -12) equal to 17.435595774 and -17.435595774.Subproblem 1
x + -12 = 17.435595774 Simplifying x + -12 = 17.435595774 Reorder the terms: -12 + x = 17.435595774 Solving -12 + x = 17.435595774 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 = 17.435595774 + 12 Combine like terms: -12 + 12 = 0 0 + x = 17.435595774 + 12 x = 17.435595774 + 12 Combine like terms: 17.435595774 + 12 = 29.435595774 x = 29.435595774 Simplifying x = 29.435595774Subproblem 2
x + -12 = -17.435595774 Simplifying x + -12 = -17.435595774 Reorder the terms: -12 + x = -17.435595774 Solving -12 + x = -17.435595774 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 = -17.435595774 + 12 Combine like terms: -12 + 12 = 0 0 + x = -17.435595774 + 12 x = -17.435595774 + 12 Combine like terms: -17.435595774 + 12 = -5.435595774 x = -5.435595774 Simplifying x = -5.435595774Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.435595774, -5.435595774}
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