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Simplifying (5 + -1x)(14 + -1x) + -25 = 0 Multiply (5 + -1x) * (14 + -1x) (5(14 + -1x) + -1x * (14 + -1x)) + -25 = 0 ((14 * 5 + -1x * 5) + -1x * (14 + -1x)) + -25 = 0 ((70 + -5x) + -1x * (14 + -1x)) + -25 = 0 (70 + -5x + (14 * -1x + -1x * -1x)) + -25 = 0 (70 + -5x + (-14x + 1x2)) + -25 = 0 Combine like terms: -5x + -14x = -19x (70 + -19x + 1x2) + -25 = 0 Reorder the terms: 70 + -25 + -19x + 1x2 = 0 Combine like terms: 70 + -25 = 45 45 + -19x + 1x2 = 0 Solving 45 + -19x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -19x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -19x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -19x + x2 = 0 + -45 -19x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -19x + x2 = -45 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -45 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -45 + 90.25 Combine like terms: -45 + 90.25 = 45.25 90.25 + -19x + x2 = 45.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + -9.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + -9.5 = 6.726812024 Simplifying x + -9.5 = 6.726812024 Reorder the terms: -9.5 + x = 6.726812024 Solving -9.5 + x = 6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 6.726812024 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 6.726812024 + 9.5 x = 6.726812024 + 9.5 Combine like terms: 6.726812024 + 9.5 = 16.226812024 x = 16.226812024 Simplifying x = 16.226812024Subproblem 2
x + -9.5 = -6.726812024 Simplifying x + -9.5 = -6.726812024 Reorder the terms: -9.5 + x = -6.726812024 Solving -9.5 + x = -6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -6.726812024 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -6.726812024 + 9.5 x = -6.726812024 + 9.5 Combine like terms: -6.726812024 + 9.5 = 2.773187976 x = 2.773187976 Simplifying x = 2.773187976Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.226812024, 2.773187976}
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