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Simplifying (x + -5)(x + -3) = 18 Reorder the terms: (-5 + x)(x + -3) = 18 Reorder the terms: (-5 + x)(-3 + x) = 18 Multiply (-5 + x) * (-3 + x) (-5(-3 + x) + x(-3 + x)) = 18 ((-3 * -5 + x * -5) + x(-3 + x)) = 18 ((15 + -5x) + x(-3 + x)) = 18 (15 + -5x + (-3 * x + x * x)) = 18 (15 + -5x + (-3x + x2)) = 18 Combine like terms: -5x + -3x = -8x (15 + -8x + x2) = 18 Solving 15 + -8x + x2 = 18 Solving for variable 'x'. Reorder the terms: 15 + -18 + -8x + x2 = 18 + -18 Combine like terms: 15 + -18 = -3 -3 + -8x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -3 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -8x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -8x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8x + x2 = 0 + 3 -8x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -8x + x2 = 3 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 3 + 16 Reorder the terms: 16 + -8x + x2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + -8x + x2 = 19 Factor a perfect square on the left side: (x + -4)(x + -4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -4) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -4 = 4.358898944 Simplifying x + -4 = 4.358898944 Reorder the terms: -4 + x = 4.358898944 Solving -4 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.358898944 + 4 x = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 x = 8.358898944 Simplifying x = 8.358898944Subproblem 2
x + -4 = -4.358898944 Simplifying x + -4 = -4.358898944 Reorder the terms: -4 + x = -4.358898944 Solving -4 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.358898944 + 4 x = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 x = -0.358898944 Simplifying x = -0.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.358898944, -0.358898944}
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