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Simplifying (x + -5)(x + 2) + 4(x + -1) = 0 Reorder the terms: (-5 + x)(x + 2) + 4(x + -1) = 0 Reorder the terms: (-5 + x)(2 + x) + 4(x + -1) = 0 Multiply (-5 + x) * (2 + x) (-5(2 + x) + x(2 + x)) + 4(x + -1) = 0 ((2 * -5 + x * -5) + x(2 + x)) + 4(x + -1) = 0 ((-10 + -5x) + x(2 + x)) + 4(x + -1) = 0 (-10 + -5x + (2 * x + x * x)) + 4(x + -1) = 0 (-10 + -5x + (2x + x2)) + 4(x + -1) = 0 Combine like terms: -5x + 2x = -3x (-10 + -3x + x2) + 4(x + -1) = 0 Reorder the terms: -10 + -3x + x2 + 4(-1 + x) = 0 -10 + -3x + x2 + (-1 * 4 + x * 4) = 0 -10 + -3x + x2 + (-4 + 4x) = 0 Reorder the terms: -10 + -4 + -3x + 4x + x2 = 0 Combine like terms: -10 + -4 = -14 -14 + -3x + 4x + x2 = 0 Combine like terms: -3x + 4x = 1x -14 + 1x + x2 = 0 Solving -14 + 1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 1x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 1x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 1x + x2 = 0 + 14 1x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 1x + x2 = 14 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 14 + 0.25 Reorder the terms: 0.25 + x + x2 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + x + x2 = 14.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 0.5 = 3.774917218 Simplifying x + 0.5 = 3.774917218 Reorder the terms: 0.5 + x = 3.774917218 Solving 0.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.774917218 + -0.5 x = 3.774917218 + -0.5 Combine like terms: 3.774917218 + -0.5 = 3.274917218 x = 3.274917218 Simplifying x = 3.274917218Subproblem 2
x + 0.5 = -3.774917218 Simplifying x + 0.5 = -3.774917218 Reorder the terms: 0.5 + x = -3.774917218 Solving 0.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.774917218 + -0.5 x = -3.774917218 + -0.5 Combine like terms: -3.774917218 + -0.5 = -4.274917218 x = -4.274917218 Simplifying x = -4.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.274917218, -4.274917218}
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