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Simplifying 48x + -1x2 = 144 Solving 48x + -1x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 48x + -1x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 48x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 144 + -48x + x2 = 0 Move the constant term to the right: Add '-144' to each side of the equation. 144 + -48x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + -48x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -48x + x2 = 0 + -144 -48x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 -48x + x2 = -144 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 = -144 + 576 Reorder the terms: 576 + -48x + x2 = -144 + 576 Combine like terms: -144 + 576 = 432 576 + -48x + x2 = 432 Factor a perfect square on the left side: (x + -24)(x + -24) = 432 Calculate the square root of the right side: 20.784609691 Break this problem into two subproblems by setting (x + -24) equal to 20.784609691 and -20.784609691.Subproblem 1
x + -24 = 20.784609691 Simplifying x + -24 = 20.784609691 Reorder the terms: -24 + x = 20.784609691 Solving -24 + x = 20.784609691 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 = 20.784609691 + 24 Combine like terms: -24 + 24 = 0 0 + x = 20.784609691 + 24 x = 20.784609691 + 24 Combine like terms: 20.784609691 + 24 = 44.784609691 x = 44.784609691 Simplifying x = 44.784609691Subproblem 2
x + -24 = -20.784609691 Simplifying x + -24 = -20.784609691 Reorder the terms: -24 + x = -20.784609691 Solving -24 + x = -20.784609691 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 = -20.784609691 + 24 Combine like terms: -24 + 24 = 0 0 + x = -20.784609691 + 24 x = -20.784609691 + 24 Combine like terms: -20.784609691 + 24 = 3.215390309 x = 3.215390309 Simplifying x = 3.215390309Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.784609691, 3.215390309}
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