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Simplifying x + -1(x + 4)(x + -2) = 8 + (x + -5) Reorder the terms: x + -1(4 + x)(x + -2) = 8 + (x + -5) Reorder the terms: x + -1(4 + x)(-2 + x) = 8 + (x + -5) Multiply (4 + x) * (-2 + x) x + -1(4(-2 + x) + x(-2 + x)) = 8 + (x + -5) x + -1((-2 * 4 + x * 4) + x(-2 + x)) = 8 + (x + -5) x + -1((-8 + 4x) + x(-2 + x)) = 8 + (x + -5) x + -1(-8 + 4x + (-2 * x + x * x)) = 8 + (x + -5) x + -1(-8 + 4x + (-2x + x2)) = 8 + (x + -5) Combine like terms: 4x + -2x = 2x x + -1(-8 + 2x + x2) = 8 + (x + -5) x + (-8 * -1 + 2x * -1 + x2 * -1) = 8 + (x + -5) x + (8 + -2x + -1x2) = 8 + (x + -5) Reorder the terms: 8 + x + -2x + -1x2 = 8 + (x + -5) Combine like terms: x + -2x = -1x 8 + -1x + -1x2 = 8 + (x + -5) Reorder the terms: 8 + -1x + -1x2 = 8 + (-5 + x) Remove parenthesis around (-5 + x) 8 + -1x + -1x2 = 8 + -5 + x Combine like terms: 8 + -5 = 3 8 + -1x + -1x2 = 3 + x Solving 8 + -1x + -1x2 = 3 + x Solving for variable 'x'. Reorder the terms: 8 + -3 + -1x + -1x + -1x2 = 3 + x + -3 + -1x Combine like terms: 8 + -3 = 5 5 + -1x + -1x + -1x2 = 3 + x + -3 + -1x Combine like terms: -1x + -1x = -2x 5 + -2x + -1x2 = 3 + x + -3 + -1x Reorder the terms: 5 + -2x + -1x2 = 3 + -3 + x + -1x Combine like terms: 3 + -3 = 0 5 + -2x + -1x2 = 0 + x + -1x 5 + -2x + -1x2 = x + -1x Combine like terms: x + -1x = 0 5 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 2x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x + x2 = 0 + 5 2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2x + x2 = 5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5 + 1 Reorder the terms: 1 + 2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2x + x2 = 6 Factor a perfect square on the left side: (x + 1)(x + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 1 = 2.449489743 Simplifying x + 1 = 2.449489743 Reorder the terms: 1 + x = 2.449489743 Solving 1 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.449489743 + -1 x = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 x = 1.449489743 Simplifying x = 1.449489743Subproblem 2
x + 1 = -2.449489743 Simplifying x + 1 = -2.449489743 Reorder the terms: 1 + x = -2.449489743 Solving 1 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.449489743 + -1 x = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 x = -3.449489743 Simplifying x = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.449489743, -3.449489743}
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