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Simplifying 15x + (-6x + 5) + -2 + -1(-1x + 3) = -1(7x + 23) * x + (3 + -2x) Reorder the terms: 15x + (5 + -6x) + -2 + -1(-1x + 3) = -1(7x + 23) * x + (3 + -2x) Remove parenthesis around (5 + -6x) 15x + 5 + -6x + -2 + -1(-1x + 3) = -1(7x + 23) * x + (3 + -2x) Reorder the terms: 15x + 5 + -6x + -2 + -1(3 + -1x) = -1(7x + 23) * x + (3 + -2x) 15x + 5 + -6x + -2 + (3 * -1 + -1x * -1) = -1(7x + 23) * x + (3 + -2x) 15x + 5 + -6x + -2 + (-3 + 1x) = -1(7x + 23) * x + (3 + -2x) Reorder the terms: 5 + -2 + -3 + 15x + -6x + 1x = -1(7x + 23) * x + (3 + -2x) Combine like terms: 5 + -2 = 3 3 + -3 + 15x + -6x + 1x = -1(7x + 23) * x + (3 + -2x) Combine like terms: 3 + -3 = 0 0 + 15x + -6x + 1x = -1(7x + 23) * x + (3 + -2x) 15x + -6x + 1x = -1(7x + 23) * x + (3 + -2x) Combine like terms: 15x + -6x = 9x 9x + 1x = -1(7x + 23) * x + (3 + -2x) Combine like terms: 9x + 1x = 10x 10x = -1(7x + 23) * x + (3 + -2x) Reorder the terms: 10x = -1(23 + 7x) * x + (3 + -2x) Reorder the terms for easier multiplication: 10x = -1x(23 + 7x) + (3 + -2x) 10x = (23 * -1x + 7x * -1x) + (3 + -2x) 10x = (-23x + -7x2) + (3 + -2x) Remove parenthesis around (3 + -2x) 10x = -23x + -7x2 + 3 + -2x Reorder the terms: 10x = 3 + -23x + -2x + -7x2 Combine like terms: -23x + -2x = -25x 10x = 3 + -25x + -7x2 Solving 10x = 3 + -25x + -7x2 Solving for variable 'x'. Reorder the terms: -3 + 10x + 25x + 7x2 = 3 + -25x + -7x2 + -3 + 25x + 7x2 Combine like terms: 10x + 25x = 35x -3 + 35x + 7x2 = 3 + -25x + -7x2 + -3 + 25x + 7x2 Reorder the terms: -3 + 35x + 7x2 = 3 + -3 + -25x + 25x + -7x2 + 7x2 Combine like terms: 3 + -3 = 0 -3 + 35x + 7x2 = 0 + -25x + 25x + -7x2 + 7x2 -3 + 35x + 7x2 = -25x + 25x + -7x2 + 7x2 Combine like terms: -25x + 25x = 0 -3 + 35x + 7x2 = 0 + -7x2 + 7x2 -3 + 35x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -3 + 35x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 5x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 5x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 5x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 5x + x2 = 0 + 0.4285714286 5x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 5x + x2 = 0.4285714286 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.4285714286 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.4285714286 + 6.25 Combine like terms: 0.4285714286 + 6.25 = 6.6785714286 6.25 + 5x + x2 = 6.6785714286 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.6785714286 Calculate the square root of the right side: 2.584293216 Break this problem into two subproblems by setting (x + 2.5) equal to 2.584293216 and -2.584293216.Subproblem 1
x + 2.5 = 2.584293216 Simplifying x + 2.5 = 2.584293216 Reorder the terms: 2.5 + x = 2.584293216 Solving 2.5 + x = 2.584293216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.584293216 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.584293216 + -2.5 x = 2.584293216 + -2.5 Combine like terms: 2.584293216 + -2.5 = 0.084293216 x = 0.084293216 Simplifying x = 0.084293216Subproblem 2
x + 2.5 = -2.584293216 Simplifying x + 2.5 = -2.584293216 Reorder the terms: 2.5 + x = -2.584293216 Solving 2.5 + x = -2.584293216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.584293216 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.584293216 + -2.5 x = -2.584293216 + -2.5 Combine like terms: -2.584293216 + -2.5 = -5.084293216 x = -5.084293216 Simplifying x = -5.084293216Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.084293216, -5.084293216}
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