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Simplifying x2 + -48x + -104 = 0 Reorder the terms: -104 + -48x + x2 = 0 Solving -104 + -48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + -48x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + -48x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -48x + x2 = 0 + 104 -48x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 -48x + x2 = 104 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 = 104 + 576 Reorder the terms: 576 + -48x + x2 = 104 + 576 Combine like terms: 104 + 576 = 680 576 + -48x + x2 = 680 Factor a perfect square on the left side: (x + -24)(x + -24) = 680 Calculate the square root of the right side: 26.076809621 Break this problem into two subproblems by setting (x + -24) equal to 26.076809621 and -26.076809621.Subproblem 1
x + -24 = 26.076809621 Simplifying x + -24 = 26.076809621 Reorder the terms: -24 + x = 26.076809621 Solving -24 + x = 26.076809621 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 = 26.076809621 + 24 Combine like terms: -24 + 24 = 0 0 + x = 26.076809621 + 24 x = 26.076809621 + 24 Combine like terms: 26.076809621 + 24 = 50.076809621 x = 50.076809621 Simplifying x = 50.076809621Subproblem 2
x + -24 = -26.076809621 Simplifying x + -24 = -26.076809621 Reorder the terms: -24 + x = -26.076809621 Solving -24 + x = -26.076809621 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 = -26.076809621 + 24 Combine like terms: -24 + 24 = 0 0 + x = -26.076809621 + 24 x = -26.076809621 + 24 Combine like terms: -26.076809621 + 24 = -2.076809621 x = -2.076809621 Simplifying x = -2.076809621Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.076809621, -2.076809621}
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