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Simplifying -1x2 + 64x + 75 = 0 Reorder the terms: 75 + 64x + -1x2 = 0 Solving 75 + 64x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -75 + -64x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -64x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -64x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -64x + x2 = 0 + 75 -64x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -64x + x2 = 75 The x term is -64x. Take half its coefficient (-32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. -64x + 1024 + x2 = 75 + 1024 Reorder the terms: 1024 + -64x + x2 = 75 + 1024 Combine like terms: 75 + 1024 = 1099 1024 + -64x + x2 = 1099 Factor a perfect square on the left side: (x + -32)(x + -32) = 1099 Calculate the square root of the right side: 33.151168909 Break this problem into two subproblems by setting (x + -32) equal to 33.151168909 and -33.151168909.Subproblem 1
x + -32 = 33.151168909 Simplifying x + -32 = 33.151168909 Reorder the terms: -32 + x = 33.151168909 Solving -32 + x = 33.151168909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = 33.151168909 + 32 Combine like terms: -32 + 32 = 0 0 + x = 33.151168909 + 32 x = 33.151168909 + 32 Combine like terms: 33.151168909 + 32 = 65.151168909 x = 65.151168909 Simplifying x = 65.151168909Subproblem 2
x + -32 = -33.151168909 Simplifying x + -32 = -33.151168909 Reorder the terms: -32 + x = -33.151168909 Solving -32 + x = -33.151168909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = -33.151168909 + 32 Combine like terms: -32 + 32 = 0 0 + x = -33.151168909 + 32 x = -33.151168909 + 32 Combine like terms: -33.151168909 + 32 = -1.151168909 x = -1.151168909 Simplifying x = -1.151168909Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.151168909, -1.151168909}
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