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Simplifying (x + 5)(x + -4) + x2 + 18 = 0 Reorder the terms: (5 + x)(x + -4) + x2 + 18 = 0 Reorder the terms: (5 + x)(-4 + x) + x2 + 18 = 0 Multiply (5 + x) * (-4 + x) (5(-4 + x) + x(-4 + x)) + x2 + 18 = 0 ((-4 * 5 + x * 5) + x(-4 + x)) + x2 + 18 = 0 ((-20 + 5x) + x(-4 + x)) + x2 + 18 = 0 (-20 + 5x + (-4 * x + x * x)) + x2 + 18 = 0 (-20 + 5x + (-4x + x2)) + x2 + 18 = 0 Combine like terms: 5x + -4x = 1x (-20 + 1x + x2) + x2 + 18 = 0 Reorder the terms: -20 + 18 + 1x + x2 + x2 = 0 Combine like terms: -20 + 18 = -2 -2 + 1x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -2 + 1x + 2x2 = 0 Solving -2 + 1x + 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'. -1 + 0.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.5x + x2 = 0 + 1 0.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.5x + x2 = 1 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + 0.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 0.25 = 1.030776406 Simplifying x + 0.25 = 1.030776406 Reorder the terms: 0.25 + x = 1.030776406 Solving 0.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.030776406 + -0.25 x = 1.030776406 + -0.25 Combine like terms: 1.030776406 + -0.25 = 0.780776406 x = 0.780776406 Simplifying x = 0.780776406Subproblem 2
x + 0.25 = -1.030776406 Simplifying x + 0.25 = -1.030776406 Reorder the terms: 0.25 + x = -1.030776406 Solving 0.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.030776406 + -0.25 x = -1.030776406 + -0.25 Combine like terms: -1.030776406 + -0.25 = -1.280776406 x = -1.280776406 Simplifying x = -1.280776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.780776406, -1.280776406}
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