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Simplifying x2 + 16x = 240 Reorder the terms: 16x + x2 = 240 Solving 16x + x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 16x + x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 16x + x2 = 0 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 = 9.435595774 x = 9.435595774 Simplifying x = 9.435595774Subproblem 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 = -25.435595774 x = -25.435595774 Simplifying x = -25.435595774Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.435595774, -25.435595774}
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