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Simplifying x2 + -1(x + -3) + -54 = 0 Reorder the terms: x2 + -1(-3 + x) + -54 = 0 x2 + (-3 * -1 + x * -1) + -54 = 0 x2 + (3 + -1x) + -54 = 0 Reorder the terms: 3 + -54 + -1x + x2 = 0 Combine like terms: 3 + -54 = -51 -51 + -1x + x2 = 0 Solving -51 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -1x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -1x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -1x + x2 = 0 + 51 -1x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -1x + x2 = 51 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 51 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 51 + 0.25 Combine like terms: 51 + 0.25 = 51.25 0.25 + -1x + x2 = 51.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -0.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -0.5 = 7.158910532 Simplifying x + -0.5 = 7.158910532 Reorder the terms: -0.5 + x = 7.158910532 Solving -0.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.158910532 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.158910532 + 0.5 x = 7.158910532 + 0.5 Combine like terms: 7.158910532 + 0.5 = 7.658910532 x = 7.658910532 Simplifying x = 7.658910532Subproblem 2
x + -0.5 = -7.158910532 Simplifying x + -0.5 = -7.158910532 Reorder the terms: -0.5 + x = -7.158910532 Solving -0.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.158910532 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.158910532 + 0.5 x = -7.158910532 + 0.5 Combine like terms: -7.158910532 + 0.5 = -6.658910532 x = -6.658910532 Simplifying x = -6.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.658910532, -6.658910532}
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