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Simplifying x * x + -1x = 63 Multiply x * x x2 + -1x = 63 Reorder the terms: -1x + x2 = 63 Solving -1x + x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + -1x + x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -1x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + -1x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -1x + x2 = 0 + 63 -1x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 -1x + x2 = 63 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 = 63 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 63 + 0.25 Combine like terms: 63 + 0.25 = 63.25 0.25 + -1x + x2 = 63.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + -0.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + -0.5 = 7.95298686 Simplifying x + -0.5 = 7.95298686 Reorder the terms: -0.5 + x = 7.95298686 Solving -0.5 + x = 7.95298686 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 = 7.95298686 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.95298686 + 0.5 x = 7.95298686 + 0.5 Combine like terms: 7.95298686 + 0.5 = 8.45298686 x = 8.45298686 Simplifying x = 8.45298686Subproblem 2
x + -0.5 = -7.95298686 Simplifying x + -0.5 = -7.95298686 Reorder the terms: -0.5 + x = -7.95298686 Solving -0.5 + x = -7.95298686 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 = -7.95298686 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.95298686 + 0.5 x = -7.95298686 + 0.5 Combine like terms: -7.95298686 + 0.5 = -7.45298686 x = -7.45298686 Simplifying x = -7.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.45298686, -7.45298686}
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