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Simplifying x2 + 32x + 256 = 128x Reorder the terms: 256 + 32x + x2 = 128x Solving 256 + 32x + x2 = 128x Solving for variable 'x'. Reorder the terms: 256 + 32x + -128x + x2 = 128x + -128x Combine like terms: 32x + -128x = -96x 256 + -96x + x2 = 128x + -128x Combine like terms: 128x + -128x = 0 256 + -96x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + -96x + -256 + x2 = 0 + -256 Reorder the terms: 256 + -256 + -96x + x2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + -96x + x2 = 0 + -256 -96x + x2 = 0 + -256 Combine like terms: 0 + -256 = -256 -96x + x2 = -256 The x term is -96x. Take half its coefficient (-48). Square it (2304) and add it to both sides. Add '2304' to each side of the equation. -96x + 2304 + x2 = -256 + 2304 Reorder the terms: 2304 + -96x + x2 = -256 + 2304 Combine like terms: -256 + 2304 = 2048 2304 + -96x + x2 = 2048 Factor a perfect square on the left side: (x + -48)(x + -48) = 2048 Calculate the square root of the right side: 45.254833996 Break this problem into two subproblems by setting (x + -48) equal to 45.254833996 and -45.254833996.Subproblem 1
x + -48 = 45.254833996 Simplifying x + -48 = 45.254833996 Reorder the terms: -48 + x = 45.254833996 Solving -48 + x = 45.254833996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = 45.254833996 + 48 Combine like terms: -48 + 48 = 0 0 + x = 45.254833996 + 48 x = 45.254833996 + 48 Combine like terms: 45.254833996 + 48 = 93.254833996 x = 93.254833996 Simplifying x = 93.254833996Subproblem 2
x + -48 = -45.254833996 Simplifying x + -48 = -45.254833996 Reorder the terms: -48 + x = -45.254833996 Solving -48 + x = -45.254833996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = -45.254833996 + 48 Combine like terms: -48 + 48 = 0 0 + x = -45.254833996 + 48 x = -45.254833996 + 48 Combine like terms: -45.254833996 + 48 = 2.745166004 x = 2.745166004 Simplifying x = 2.745166004Solution
The solution to the problem is based on the solutions from the subproblems. x = {93.254833996, 2.745166004}
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