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Simplifying x2 + -48x + 384 = 0 Reorder the terms: 384 + -48x + x2 = 0 Solving 384 + -48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-384' to each side of the equation. 384 + -48x + -384 + x2 = 0 + -384 Reorder the terms: 384 + -384 + -48x + x2 = 0 + -384 Combine like terms: 384 + -384 = 0 0 + -48x + x2 = 0 + -384 -48x + x2 = 0 + -384 Combine like terms: 0 + -384 = -384 -48x + x2 = -384 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 = -384 + 576 Reorder the terms: 576 + -48x + x2 = -384 + 576 Combine like terms: -384 + 576 = 192 576 + -48x + x2 = 192 Factor a perfect square on the left side: (x + -24)(x + -24) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (x + -24) equal to 13.856406461 and -13.856406461.Subproblem 1
x + -24 = 13.856406461 Simplifying x + -24 = 13.856406461 Reorder the terms: -24 + x = 13.856406461 Solving -24 + x = 13.856406461 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 = 13.856406461 + 24 Combine like terms: -24 + 24 = 0 0 + x = 13.856406461 + 24 x = 13.856406461 + 24 Combine like terms: 13.856406461 + 24 = 37.856406461 x = 37.856406461 Simplifying x = 37.856406461Subproblem 2
x + -24 = -13.856406461 Simplifying x + -24 = -13.856406461 Reorder the terms: -24 + x = -13.856406461 Solving -24 + x = -13.856406461 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 = -13.856406461 + 24 Combine like terms: -24 + 24 = 0 0 + x = -13.856406461 + 24 x = -13.856406461 + 24 Combine like terms: -13.856406461 + 24 = 10.143593539 x = 10.143593539 Simplifying x = 10.143593539Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.856406461, 10.143593539}
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