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Simplifying 0 = x2 + -64x + 538 Reorder the terms: 0 = 538 + -64x + x2 Solving 0 = 538 + -64x + x2 Solving for variable 'x'. Combine like terms: 0 + -538 = -538 -538 + 64x + -1x2 = 538 + -64x + x2 + -538 + 64x + -1x2 Reorder the terms: -538 + 64x + -1x2 = 538 + -538 + -64x + 64x + x2 + -1x2 Combine like terms: 538 + -538 = 0 -538 + 64x + -1x2 = 0 + -64x + 64x + x2 + -1x2 -538 + 64x + -1x2 = -64x + 64x + x2 + -1x2 Combine like terms: -64x + 64x = 0 -538 + 64x + -1x2 = 0 + x2 + -1x2 -538 + 64x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -538 + 64x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 538 + -64x + x2 = 0 Move the constant term to the right: Add '-538' to each side of the equation. 538 + -64x + -538 + x2 = 0 + -538 Reorder the terms: 538 + -538 + -64x + x2 = 0 + -538 Combine like terms: 538 + -538 = 0 0 + -64x + x2 = 0 + -538 -64x + x2 = 0 + -538 Combine like terms: 0 + -538 = -538 -64x + x2 = -538 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 = -538 + 1024 Reorder the terms: 1024 + -64x + x2 = -538 + 1024 Combine like terms: -538 + 1024 = 486 1024 + -64x + x2 = 486 Factor a perfect square on the left side: (x + -32)(x + -32) = 486 Calculate the square root of the right side: 22.045407685 Break this problem into two subproblems by setting (x + -32) equal to 22.045407685 and -22.045407685.Subproblem 1
x + -32 = 22.045407685 Simplifying x + -32 = 22.045407685 Reorder the terms: -32 + x = 22.045407685 Solving -32 + x = 22.045407685 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 = 22.045407685 + 32 Combine like terms: -32 + 32 = 0 0 + x = 22.045407685 + 32 x = 22.045407685 + 32 Combine like terms: 22.045407685 + 32 = 54.045407685 x = 54.045407685 Simplifying x = 54.045407685Subproblem 2
x + -32 = -22.045407685 Simplifying x + -32 = -22.045407685 Reorder the terms: -32 + x = -22.045407685 Solving -32 + x = -22.045407685 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 = -22.045407685 + 32 Combine like terms: -32 + 32 = 0 0 + x = -22.045407685 + 32 x = -22.045407685 + 32 Combine like terms: -22.045407685 + 32 = 9.954592315 x = 9.954592315 Simplifying x = 9.954592315Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.045407685, 9.954592315}
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