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Simplifying x2 + -24x + 144 + -64x + -64 = 0 Reorder the terms: 144 + -64 + -24x + -64x + x2 = 0 Combine like terms: 144 + -64 = 80 80 + -24x + -64x + x2 = 0 Combine like terms: -24x + -64x = -88x 80 + -88x + x2 = 0 Solving 80 + -88x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -88x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -88x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -88x + x2 = 0 + -80 -88x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -88x + x2 = -80 The x term is -88x. Take half its coefficient (-44). Square it (1936) and add it to both sides. Add '1936' to each side of the equation. -88x + 1936 + x2 = -80 + 1936 Reorder the terms: 1936 + -88x + x2 = -80 + 1936 Combine like terms: -80 + 1936 = 1856 1936 + -88x + x2 = 1856 Factor a perfect square on the left side: (x + -44)(x + -44) = 1856 Calculate the square root of the right side: 43.081318457 Break this problem into two subproblems by setting (x + -44) equal to 43.081318457 and -43.081318457.Subproblem 1
x + -44 = 43.081318457 Simplifying x + -44 = 43.081318457 Reorder the terms: -44 + x = 43.081318457 Solving -44 + x = 43.081318457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44' to each side of the equation. -44 + 44 + x = 43.081318457 + 44 Combine like terms: -44 + 44 = 0 0 + x = 43.081318457 + 44 x = 43.081318457 + 44 Combine like terms: 43.081318457 + 44 = 87.081318457 x = 87.081318457 Simplifying x = 87.081318457Subproblem 2
x + -44 = -43.081318457 Simplifying x + -44 = -43.081318457 Reorder the terms: -44 + x = -43.081318457 Solving -44 + x = -43.081318457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44' to each side of the equation. -44 + 44 + x = -43.081318457 + 44 Combine like terms: -44 + 44 = 0 0 + x = -43.081318457 + 44 x = -43.081318457 + 44 Combine like terms: -43.081318457 + 44 = 0.918681543 x = 0.918681543 Simplifying x = 0.918681543Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.081318457, 0.918681543}
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