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Simplifying x2 + -6x + 1 = 1.5x + 6 Reorder the terms: 1 + -6x + x2 = 1.5x + 6 Reorder the terms: 1 + -6x + x2 = 6 + 1.5x Solving 1 + -6x + x2 = 6 + 1.5x Solving for variable 'x'. Reorder the terms: 1 + -6 + -6x + -1.5x + x2 = 6 + 1.5x + -6 + -1.5x Combine like terms: 1 + -6 = -5 -5 + -6x + -1.5x + x2 = 6 + 1.5x + -6 + -1.5x Combine like terms: -6x + -1.5x = -7.5x -5 + -7.5x + x2 = 6 + 1.5x + -6 + -1.5x Reorder the terms: -5 + -7.5x + x2 = 6 + -6 + 1.5x + -1.5x Combine like terms: 6 + -6 = 0 -5 + -7.5x + x2 = 0 + 1.5x + -1.5x -5 + -7.5x + x2 = 1.5x + -1.5x Combine like terms: 1.5x + -1.5x = 0.0 -5 + -7.5x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -7.5x + 5 + x2 = 0.0 + 5 Reorder the terms: -5 + 5 + -7.5x + x2 = 0.0 + 5 Combine like terms: -5 + 5 = 0 0 + -7.5x + x2 = 0.0 + 5 -7.5x + x2 = 0.0 + 5 Combine like terms: 0.0 + 5 = 5 -7.5x + x2 = 5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 5 + 14.0625 Combine like terms: 5 + 14.0625 = 19.0625 14.0625 + -7.5x + x2 = 19.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (x + -3.75) equal to 4.366062299 and -4.366062299.Subproblem 1
x + -3.75 = 4.366062299 Simplifying x + -3.75 = 4.366062299 Reorder the terms: -3.75 + x = 4.366062299 Solving -3.75 + x = 4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 4.366062299 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.366062299 + 3.75 x = 4.366062299 + 3.75 Combine like terms: 4.366062299 + 3.75 = 8.116062299 x = 8.116062299 Simplifying x = 8.116062299Subproblem 2
x + -3.75 = -4.366062299 Simplifying x + -3.75 = -4.366062299 Reorder the terms: -3.75 + x = -4.366062299 Solving -3.75 + x = -4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -4.366062299 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.366062299 + 3.75 x = -4.366062299 + 3.75 Combine like terms: -4.366062299 + 3.75 = -0.616062299 x = -0.616062299 Simplifying x = -0.616062299Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.116062299, -0.616062299}
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