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Simplifying x2 + -24x + 64 = 0 Reorder the terms: 64 + -24x + x2 = 0 Solving 64 + -24x + 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 + -24x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -24x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -24x + x2 = 0 + -64 -24x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -24x + x2 = -64 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -64 + 144 Reorder the terms: 144 + -24x + x2 = -64 + 144 Combine like terms: -64 + 144 = 80 144 + -24x + x2 = 80 Factor a perfect square on the left side: (x + -12)(x + -12) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -12) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -12 = 8.94427191 Simplifying x + -12 = 8.94427191 Reorder the terms: -12 + x = 8.94427191 Solving -12 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 8.94427191 + 12 Combine like terms: -12 + 12 = 0 0 + x = 8.94427191 + 12 x = 8.94427191 + 12 Combine like terms: 8.94427191 + 12 = 20.94427191 x = 20.94427191 Simplifying x = 20.94427191Subproblem 2
x + -12 = -8.94427191 Simplifying x + -12 = -8.94427191 Reorder the terms: -12 + x = -8.94427191 Solving -12 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -8.94427191 + 12 Combine like terms: -12 + 12 = 0 0 + x = -8.94427191 + 12 x = -8.94427191 + 12 Combine like terms: -8.94427191 + 12 = 3.05572809 x = 3.05572809 Simplifying x = 3.05572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.94427191, 3.05572809}
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