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Simplifying x2 + -112x + -2352 = 0 Reorder the terms: -2352 + -112x + x2 = 0 Solving -2352 + -112x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2352' to each side of the equation. -2352 + -112x + 2352 + x2 = 0 + 2352 Reorder the terms: -2352 + 2352 + -112x + x2 = 0 + 2352 Combine like terms: -2352 + 2352 = 0 0 + -112x + x2 = 0 + 2352 -112x + x2 = 0 + 2352 Combine like terms: 0 + 2352 = 2352 -112x + x2 = 2352 The x term is -112x. Take half its coefficient (-56). Square it (3136) and add it to both sides. Add '3136' to each side of the equation. -112x + 3136 + x2 = 2352 + 3136 Reorder the terms: 3136 + -112x + x2 = 2352 + 3136 Combine like terms: 2352 + 3136 = 5488 3136 + -112x + x2 = 5488 Factor a perfect square on the left side: (x + -56)(x + -56) = 5488 Calculate the square root of the right side: 74.08103671 Break this problem into two subproblems by setting (x + -56) equal to 74.08103671 and -74.08103671.Subproblem 1
x + -56 = 74.08103671 Simplifying x + -56 = 74.08103671 Reorder the terms: -56 + x = 74.08103671 Solving -56 + x = 74.08103671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = 74.08103671 + 56 Combine like terms: -56 + 56 = 0 0 + x = 74.08103671 + 56 x = 74.08103671 + 56 Combine like terms: 74.08103671 + 56 = 130.08103671 x = 130.08103671 Simplifying x = 130.08103671Subproblem 2
x + -56 = -74.08103671 Simplifying x + -56 = -74.08103671 Reorder the terms: -56 + x = -74.08103671 Solving -56 + x = -74.08103671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = -74.08103671 + 56 Combine like terms: -56 + 56 = 0 0 + x = -74.08103671 + 56 x = -74.08103671 + 56 Combine like terms: -74.08103671 + 56 = -18.08103671 x = -18.08103671 Simplifying x = -18.08103671Solution
The solution to the problem is based on the solutions from the subproblems. x = {130.08103671, -18.08103671}
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