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Simplifying x2 + 2x + 1 = 64(x + -2) Reorder the terms: 1 + 2x + x2 = 64(x + -2) Reorder the terms: 1 + 2x + x2 = 64(-2 + x) 1 + 2x + x2 = (-2 * 64 + x * 64) 1 + 2x + x2 = (-128 + 64x) Solving 1 + 2x + x2 = -128 + 64x Solving for variable 'x'. Reorder the terms: 1 + 128 + 2x + -64x + x2 = -128 + 64x + 128 + -64x Combine like terms: 1 + 128 = 129 129 + 2x + -64x + x2 = -128 + 64x + 128 + -64x Combine like terms: 2x + -64x = -62x 129 + -62x + x2 = -128 + 64x + 128 + -64x Reorder the terms: 129 + -62x + x2 = -128 + 128 + 64x + -64x Combine like terms: -128 + 128 = 0 129 + -62x + x2 = 0 + 64x + -64x 129 + -62x + x2 = 64x + -64x Combine like terms: 64x + -64x = 0 129 + -62x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-129' to each side of the equation. 129 + -62x + -129 + x2 = 0 + -129 Reorder the terms: 129 + -129 + -62x + x2 = 0 + -129 Combine like terms: 129 + -129 = 0 0 + -62x + x2 = 0 + -129 -62x + x2 = 0 + -129 Combine like terms: 0 + -129 = -129 -62x + x2 = -129 The x term is -62x. Take half its coefficient (-31). Square it (961) and add it to both sides. Add '961' to each side of the equation. -62x + 961 + x2 = -129 + 961 Reorder the terms: 961 + -62x + x2 = -129 + 961 Combine like terms: -129 + 961 = 832 961 + -62x + x2 = 832 Factor a perfect square on the left side: (x + -31)(x + -31) = 832 Calculate the square root of the right side: 28.844410204 Break this problem into two subproblems by setting (x + -31) equal to 28.844410204 and -28.844410204.Subproblem 1
x + -31 = 28.844410204 Simplifying x + -31 = 28.844410204 Reorder the terms: -31 + x = 28.844410204 Solving -31 + x = 28.844410204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = 28.844410204 + 31 Combine like terms: -31 + 31 = 0 0 + x = 28.844410204 + 31 x = 28.844410204 + 31 Combine like terms: 28.844410204 + 31 = 59.844410204 x = 59.844410204 Simplifying x = 59.844410204Subproblem 2
x + -31 = -28.844410204 Simplifying x + -31 = -28.844410204 Reorder the terms: -31 + x = -28.844410204 Solving -31 + x = -28.844410204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + x = -28.844410204 + 31 Combine like terms: -31 + 31 = 0 0 + x = -28.844410204 + 31 x = -28.844410204 + 31 Combine like terms: -28.844410204 + 31 = 2.155589796 x = 2.155589796 Simplifying x = 2.155589796Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.844410204, 2.155589796}
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