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Simplifying x2 + 24 + 6x + 4 + 10x + 10 = 180 Reorder the terms: 24 + 4 + 10 + 6x + 10x + x2 = 180 Combine like terms: 24 + 4 = 28 28 + 10 + 6x + 10x + x2 = 180 Combine like terms: 28 + 10 = 38 38 + 6x + 10x + x2 = 180 Combine like terms: 6x + 10x = 16x 38 + 16x + x2 = 180 Solving 38 + 16x + x2 = 180 Solving for variable 'x'. Reorder the terms: 38 + -180 + 16x + x2 = 180 + -180 Combine like terms: 38 + -180 = -142 -142 + 16x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -142 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + 16x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + 16x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + 16x + x2 = 0 + 142 16x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 16x + x2 = 142 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 = 142 + 64 Reorder the terms: 64 + 16x + x2 = 142 + 64 Combine like terms: 142 + 64 = 206 64 + 16x + x2 = 206 Factor a perfect square on the left side: (x + 8)(x + 8) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (x + 8) equal to 14.352700094 and -14.352700094.Subproblem 1
x + 8 = 14.352700094 Simplifying x + 8 = 14.352700094 Reorder the terms: 8 + x = 14.352700094 Solving 8 + x = 14.352700094 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 = 14.352700094 + -8 Combine like terms: 8 + -8 = 0 0 + x = 14.352700094 + -8 x = 14.352700094 + -8 Combine like terms: 14.352700094 + -8 = 6.352700094 x = 6.352700094 Simplifying x = 6.352700094Subproblem 2
x + 8 = -14.352700094 Simplifying x + 8 = -14.352700094 Reorder the terms: 8 + x = -14.352700094 Solving 8 + x = -14.352700094 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 = -14.352700094 + -8 Combine like terms: 8 + -8 = 0 0 + x = -14.352700094 + -8 x = -14.352700094 + -8 Combine like terms: -14.352700094 + -8 = -22.352700094 x = -22.352700094 Simplifying x = -22.352700094Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.352700094, -22.352700094}
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