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Simplifying 0 = x2 + -48x + 64 Reorder the terms: 0 = 64 + -48x + x2 Solving 0 = 64 + -48x + x2 Solving for variable 'x'. Combine like terms: 0 + -64 = -64 -64 + 48x + -1x2 = 64 + -48x + x2 + -64 + 48x + -1x2 Reorder the terms: -64 + 48x + -1x2 = 64 + -64 + -48x + 48x + x2 + -1x2 Combine like terms: 64 + -64 = 0 -64 + 48x + -1x2 = 0 + -48x + 48x + x2 + -1x2 -64 + 48x + -1x2 = -48x + 48x + x2 + -1x2 Combine like terms: -48x + 48x = 0 -64 + 48x + -1x2 = 0 + x2 + -1x2 -64 + 48x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -64 + 48x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 64 + -48x + x2 = 0 Move the constant term to the right: Add '-64' to each side of the equation. 64 + -48x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -48x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -48x + x2 = 0 + -64 -48x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -48x + x2 = -64 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = -64 + 576 Reorder the terms: 576 + -48x + x2 = -64 + 576 Combine like terms: -64 + 576 = 512 576 + -48x + x2 = 512 Factor a perfect square on the left side: (x + -24)(x + -24) = 512 Calculate the square root of the right side: 22.627416998 Break this problem into two subproblems by setting (x + -24) equal to 22.627416998 and -22.627416998.Subproblem 1
x + -24 = 22.627416998 Simplifying x + -24 = 22.627416998 Reorder the terms: -24 + x = 22.627416998 Solving -24 + x = 22.627416998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 22.627416998 + 24 Combine like terms: -24 + 24 = 0 0 + x = 22.627416998 + 24 x = 22.627416998 + 24 Combine like terms: 22.627416998 + 24 = 46.627416998 x = 46.627416998 Simplifying x = 46.627416998Subproblem 2
x + -24 = -22.627416998 Simplifying x + -24 = -22.627416998 Reorder the terms: -24 + x = -22.627416998 Solving -24 + x = -22.627416998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -22.627416998 + 24 Combine like terms: -24 + 24 = 0 0 + x = -22.627416998 + 24 x = -22.627416998 + 24 Combine like terms: -22.627416998 + 24 = 1.372583002 x = 1.372583002 Simplifying x = 1.372583002Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.627416998, 1.372583002}
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