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Simplifying (1x + 3)(2x + -1) + -207 = 0 Reorder the terms: (3 + 1x)(2x + -1) + -207 = 0 Reorder the terms: (3 + 1x)(-1 + 2x) + -207 = 0 Multiply (3 + 1x) * (-1 + 2x) (3(-1 + 2x) + 1x * (-1 + 2x)) + -207 = 0 ((-1 * 3 + 2x * 3) + 1x * (-1 + 2x)) + -207 = 0 ((-3 + 6x) + 1x * (-1 + 2x)) + -207 = 0 (-3 + 6x + (-1 * 1x + 2x * 1x)) + -207 = 0 (-3 + 6x + (-1x + 2x2)) + -207 = 0 Combine like terms: 6x + -1x = 5x (-3 + 5x + 2x2) + -207 = 0 Reorder the terms: -3 + -207 + 5x + 2x2 = 0 Combine like terms: -3 + -207 = -210 -210 + 5x + 2x2 = 0 Solving -210 + 5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -105 + 2.5x + x2 = 0 Move the constant term to the right: Add '105' to each side of the equation. -105 + 2.5x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 2.5x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 2.5x + x2 = 0 + 105 2.5x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 2.5x + x2 = 105 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 105 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 105 + 1.5625 Combine like terms: 105 + 1.5625 = 106.5625 1.5625 + 2.5x + x2 = 106.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 106.5625 Calculate the square root of the right side: 10.322911411 Break this problem into two subproblems by setting (x + 1.25) equal to 10.322911411 and -10.322911411.Subproblem 1
x + 1.25 = 10.322911411 Simplifying x + 1.25 = 10.322911411 Reorder the terms: 1.25 + x = 10.322911411 Solving 1.25 + x = 10.322911411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 10.322911411 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 10.322911411 + -1.25 x = 10.322911411 + -1.25 Combine like terms: 10.322911411 + -1.25 = 9.072911411 x = 9.072911411 Simplifying x = 9.072911411Subproblem 2
x + 1.25 = -10.322911411 Simplifying x + 1.25 = -10.322911411 Reorder the terms: 1.25 + x = -10.322911411 Solving 1.25 + x = -10.322911411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -10.322911411 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -10.322911411 + -1.25 x = -10.322911411 + -1.25 Combine like terms: -10.322911411 + -1.25 = -11.572911411 x = -11.572911411 Simplifying x = -11.572911411Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.072911411, -11.572911411}
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