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Simplifying x2 + x + -64 = 0 Reorder the terms: -64 + x + x2 = 0 Solving -64 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + x + x2 = 0 + 64 x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 x + x2 = 64 The x term is x. 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. x + 0.25 + x2 = 64 + 0.25 Reorder the terms: 0.25 + x + x2 = 64 + 0.25 Combine like terms: 64 + 0.25 = 64.25 0.25 + x + x2 = 64.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + 0.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + 0.5 = 8.015609771 Simplifying x + 0.5 = 8.015609771 Reorder the terms: 0.5 + x = 8.015609771 Solving 0.5 + x = 8.015609771 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 = 8.015609771 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.015609771 + -0.5 x = 8.015609771 + -0.5 Combine like terms: 8.015609771 + -0.5 = 7.515609771 x = 7.515609771 Simplifying x = 7.515609771Subproblem 2
x + 0.5 = -8.015609771 Simplifying x + 0.5 = -8.015609771 Reorder the terms: 0.5 + x = -8.015609771 Solving 0.5 + x = -8.015609771 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 = -8.015609771 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.015609771 + -0.5 x = -8.015609771 + -0.5 Combine like terms: -8.015609771 + -0.5 = -8.515609771 x = -8.515609771 Simplifying x = -8.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.515609771, -8.515609771}
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