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Simplifying (x + 35)(x + 10) = 1260 Reorder the terms: (35 + x)(x + 10) = 1260 Reorder the terms: (35 + x)(10 + x) = 1260 Multiply (35 + x) * (10 + x) (35(10 + x) + x(10 + x)) = 1260 ((10 * 35 + x * 35) + x(10 + x)) = 1260 ((350 + 35x) + x(10 + x)) = 1260 (350 + 35x + (10 * x + x * x)) = 1260 (350 + 35x + (10x + x2)) = 1260 Combine like terms: 35x + 10x = 45x (350 + 45x + x2) = 1260 Solving 350 + 45x + x2 = 1260 Solving for variable 'x'. Reorder the terms: 350 + -1260 + 45x + x2 = 1260 + -1260 Combine like terms: 350 + -1260 = -910 -910 + 45x + x2 = 1260 + -1260 Combine like terms: 1260 + -1260 = 0 -910 + 45x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '910' to each side of the equation. -910 + 45x + 910 + x2 = 0 + 910 Reorder the terms: -910 + 910 + 45x + x2 = 0 + 910 Combine like terms: -910 + 910 = 0 0 + 45x + x2 = 0 + 910 45x + x2 = 0 + 910 Combine like terms: 0 + 910 = 910 45x + x2 = 910 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = 910 + 506.25 Reorder the terms: 506.25 + 45x + x2 = 910 + 506.25 Combine like terms: 910 + 506.25 = 1416.25 506.25 + 45x + x2 = 1416.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 1416.25 Calculate the square root of the right side: 37.633097135 Break this problem into two subproblems by setting (x + 22.5) equal to 37.633097135 and -37.633097135.Subproblem 1
x + 22.5 = 37.633097135 Simplifying x + 22.5 = 37.633097135 Reorder the terms: 22.5 + x = 37.633097135 Solving 22.5 + x = 37.633097135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 37.633097135 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 37.633097135 + -22.5 x = 37.633097135 + -22.5 Combine like terms: 37.633097135 + -22.5 = 15.133097135 x = 15.133097135 Simplifying x = 15.133097135Subproblem 2
x + 22.5 = -37.633097135 Simplifying x + 22.5 = -37.633097135 Reorder the terms: 22.5 + x = -37.633097135 Solving 22.5 + x = -37.633097135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -37.633097135 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -37.633097135 + -22.5 x = -37.633097135 + -22.5 Combine like terms: -37.633097135 + -22.5 = -60.133097135 x = -60.133097135 Simplifying x = -60.133097135Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.133097135, -60.133097135}
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