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Simplifying x2 + -16x + -240 = 0 Reorder the terms: -240 + -16x + x2 = 0 Solving -240 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + -16x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -16x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -16x + x2 = 0 + 240 -16x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -16x + x2 = 240 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 240 + 64 Reorder the terms: 64 + -16x + x2 = 240 + 64 Combine like terms: 240 + 64 = 304 64 + -16x + x2 = 304 Factor a perfect square on the left side: (x + -8)(x + -8) = 304 Calculate the square root of the right side: 17.435595774 Break this problem into two subproblems by setting (x + -8) equal to 17.435595774 and -17.435595774.Subproblem 1
x + -8 = 17.435595774 Simplifying x + -8 = 17.435595774 Reorder the terms: -8 + x = 17.435595774 Solving -8 + x = 17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 17.435595774 + 8 Combine like terms: -8 + 8 = 0 0 + x = 17.435595774 + 8 x = 17.435595774 + 8 Combine like terms: 17.435595774 + 8 = 25.435595774 x = 25.435595774 Simplifying x = 25.435595774Subproblem 2
x + -8 = -17.435595774 Simplifying x + -8 = -17.435595774 Reorder the terms: -8 + x = -17.435595774 Solving -8 + x = -17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -17.435595774 + 8 Combine like terms: -8 + 8 = 0 0 + x = -17.435595774 + 8 x = -17.435595774 + 8 Combine like terms: -17.435595774 + 8 = -9.435595774 x = -9.435595774 Simplifying x = -9.435595774Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.435595774, -9.435595774}
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