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Simplifying x2 + -8x + 5 = 25x + -5 Reorder the terms: 5 + -8x + x2 = 25x + -5 Reorder the terms: 5 + -8x + x2 = -5 + 25x Solving 5 + -8x + x2 = -5 + 25x Solving for variable 'x'. Reorder the terms: 5 + 5 + -8x + -25x + x2 = -5 + 25x + 5 + -25x Combine like terms: 5 + 5 = 10 10 + -8x + -25x + x2 = -5 + 25x + 5 + -25x Combine like terms: -8x + -25x = -33x 10 + -33x + x2 = -5 + 25x + 5 + -25x Reorder the terms: 10 + -33x + x2 = -5 + 5 + 25x + -25x Combine like terms: -5 + 5 = 0 10 + -33x + x2 = 0 + 25x + -25x 10 + -33x + x2 = 25x + -25x Combine like terms: 25x + -25x = 0 10 + -33x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -33x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -33x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -33x + x2 = 0 + -10 -33x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -33x + x2 = -10 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = -10 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -10 + 272.25 Combine like terms: -10 + 272.25 = 262.25 272.25 + -33x + x2 = 262.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 262.25 Calculate the square root of the right side: 16.194134741 Break this problem into two subproblems by setting (x + -16.5) equal to 16.194134741 and -16.194134741.Subproblem 1
x + -16.5 = 16.194134741 Simplifying x + -16.5 = 16.194134741 Reorder the terms: -16.5 + x = 16.194134741 Solving -16.5 + x = 16.194134741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 16.194134741 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 16.194134741 + 16.5 x = 16.194134741 + 16.5 Combine like terms: 16.194134741 + 16.5 = 32.694134741 x = 32.694134741 Simplifying x = 32.694134741Subproblem 2
x + -16.5 = -16.194134741 Simplifying x + -16.5 = -16.194134741 Reorder the terms: -16.5 + x = -16.194134741 Solving -16.5 + x = -16.194134741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -16.194134741 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -16.194134741 + 16.5 x = -16.194134741 + 16.5 Combine like terms: -16.194134741 + 16.5 = 0.305865259 x = 0.305865259 Simplifying x = 0.305865259Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.694134741, 0.305865259}
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