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Simplifying -7.5x + -2 = 1 + -1x2 Reorder the terms: -2 + -7.5x = 1 + -1x2 Solving -2 + -7.5x = 1 + -1x2 Solving for variable 'x'. Reorder the terms: -2 + -1 + -7.5x + x2 = 1 + -1x2 + -1 + x2 Combine like terms: -2 + -1 = -3 -3 + -7.5x + x2 = 1 + -1x2 + -1 + x2 Reorder the terms: -3 + -7.5x + x2 = 1 + -1 + -1x2 + x2 Combine like terms: 1 + -1 = 0 -3 + -7.5x + x2 = 0 + -1x2 + x2 -3 + -7.5x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -3 + -7.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -7.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -7.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7.5x + x2 = 0 + 3 -7.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -7.5x + x2 = 3 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 = 3 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 3 + 14.0625 Combine like terms: 3 + 14.0625 = 17.0625 14.0625 + -7.5x + x2 = 17.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (x + -3.75) equal to 4.13067791 and -4.13067791.Subproblem 1
x + -3.75 = 4.13067791 Simplifying x + -3.75 = 4.13067791 Reorder the terms: -3.75 + x = 4.13067791 Solving -3.75 + x = 4.13067791 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 = 4.13067791 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.13067791 + 3.75 x = 4.13067791 + 3.75 Combine like terms: 4.13067791 + 3.75 = 7.88067791 x = 7.88067791 Simplifying x = 7.88067791Subproblem 2
x + -3.75 = -4.13067791 Simplifying x + -3.75 = -4.13067791 Reorder the terms: -3.75 + x = -4.13067791 Solving -3.75 + x = -4.13067791 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 = -4.13067791 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.13067791 + 3.75 x = -4.13067791 + 3.75 Combine like terms: -4.13067791 + 3.75 = -0.38067791 x = -0.38067791 Simplifying x = -0.38067791Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.88067791, -0.38067791}
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