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Simplifying 48x = 496 + x2 Solving 48x = 496 + x2 Solving for variable 'x'. Reorder the terms: -496 + 48x + -1x2 = 496 + x2 + -496 + -1x2 Reorder the terms: -496 + 48x + -1x2 = 496 + -496 + x2 + -1x2 Combine like terms: 496 + -496 = 0 -496 + 48x + -1x2 = 0 + x2 + -1x2 -496 + 48x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -496 + 48x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 496 + -48x + x2 = 0 Move the constant term to the right: Add '-496' to each side of the equation. 496 + -48x + -496 + x2 = 0 + -496 Reorder the terms: 496 + -496 + -48x + x2 = 0 + -496 Combine like terms: 496 + -496 = 0 0 + -48x + x2 = 0 + -496 -48x + x2 = 0 + -496 Combine like terms: 0 + -496 = -496 -48x + x2 = -496 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 = -496 + 576 Reorder the terms: 576 + -48x + x2 = -496 + 576 Combine like terms: -496 + 576 = 80 576 + -48x + x2 = 80 Factor a perfect square on the left side: (x + -24)(x + -24) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -24) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -24 = 8.94427191 Simplifying x + -24 = 8.94427191 Reorder the terms: -24 + x = 8.94427191 Solving -24 + x = 8.94427191 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 = 8.94427191 + 24 Combine like terms: -24 + 24 = 0 0 + x = 8.94427191 + 24 x = 8.94427191 + 24 Combine like terms: 8.94427191 + 24 = 32.94427191 x = 32.94427191 Simplifying x = 32.94427191Subproblem 2
x + -24 = -8.94427191 Simplifying x + -24 = -8.94427191 Reorder the terms: -24 + x = -8.94427191 Solving -24 + x = -8.94427191 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 = -8.94427191 + 24 Combine like terms: -24 + 24 = 0 0 + x = -8.94427191 + 24 x = -8.94427191 + 24 Combine like terms: -8.94427191 + 24 = 15.05572809 x = 15.05572809 Simplifying x = 15.05572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.94427191, 15.05572809}
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