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Simplifying x2 + (64x + -1x) + 64 = 0 Combine like terms: 64x + -1x = 63x x2 + (63x) + 64 = 0 x2 + (63x) + 64 = 0 Reorder the terms: 64 + (63x) + x2 = 0 Solving 64 + (63x) + 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 + (63x) + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + (63x) + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + (63x) + x2 = 0 + -64 (63x) + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 (63x) + x2 = -64 The x term is (63x). Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. (63x) + 992.25 + x2 = -64 + 992.25 Reorder the terms: 992.25 + (63x) + x2 = -64 + 992.25 Combine like terms: -64 + 992.25 = 928.25 992.25 + (63x) + x2 = 928.25 Factor a perfect square on the left side: (x + 31.5)(x + 31.5) = 928.25 Calculate the square root of the right side: 30.467195473 Break this problem into two subproblems by setting (x + 31.5) equal to 30.467195473 and -30.467195473.Subproblem 1
x + 31.5 = 30.467195473 Simplifying x + 31.5 = 30.467195473 Reorder the terms: 31.5 + x = 30.467195473 Solving 31.5 + x = 30.467195473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 30.467195473 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 30.467195473 + -31.5 x = 30.467195473 + -31.5 Combine like terms: 30.467195473 + -31.5 = -1.032804527 x = -1.032804527 Simplifying x = -1.032804527Subproblem 2
x + 31.5 = -30.467195473 Simplifying x + 31.5 = -30.467195473 Reorder the terms: 31.5 + x = -30.467195473 Solving 31.5 + x = -30.467195473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -30.467195473 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -30.467195473 + -31.5 x = -30.467195473 + -31.5 Combine like terms: -30.467195473 + -31.5 = -61.967195473 x = -61.967195473 Simplifying x = -61.967195473Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.032804527, -61.967195473}
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