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Simplifying x + 1 + -2(x + 2)(x + -2) = 0 Reorder the terms: x + 1 + -2(2 + x)(x + -2) = 0 Reorder the terms: x + 1 + -2(2 + x)(-2 + x) = 0 Multiply (2 + x) * (-2 + x) x + 1 + -2(2(-2 + x) + x(-2 + x)) = 0 x + 1 + -2((-2 * 2 + x * 2) + x(-2 + x)) = 0 x + 1 + -2((-4 + 2x) + x(-2 + x)) = 0 x + 1 + -2(-4 + 2x + (-2 * x + x * x)) = 0 x + 1 + -2(-4 + 2x + (-2x + x2)) = 0 Combine like terms: 2x + -2x = 0 x + 1 + -2(-4 + 0 + x2) = 0 x + 1 + -2(-4 + x2) = 0 x + 1 + (-4 * -2 + x2 * -2) = 0 x + 1 + (8 + -2x2) = 0 Reorder the terms: 1 + 8 + x + -2x2 = 0 Combine like terms: 1 + 8 = 9 9 + x + -2x2 = 0 Solving 9 + x + -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'. -4.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -0.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -0.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -0.5x + x2 = 0 + 4.5 -0.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -0.5x + x2 = 4.5 The x term is x. 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. -0.5x + 0.25 + x2 = 4.5 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + -0.5x + x2 = 4.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + 0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + 0.5 = 2.179449472 Simplifying x + 0.5 = 2.179449472 Reorder the terms: 0.5 + x = 2.179449472 Solving 0.5 + x = 2.179449472 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 = 2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.179449472 + -0.5 x = 2.179449472 + -0.5 Combine like terms: 2.179449472 + -0.5 = 1.679449472 x = 1.679449472 Simplifying x = 1.679449472Subproblem 2
x + 0.5 = -2.179449472 Simplifying x + 0.5 = -2.179449472 Reorder the terms: 0.5 + x = -2.179449472 Solving 0.5 + x = -2.179449472 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 = -2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.179449472 + -0.5 x = -2.179449472 + -0.5 Combine like terms: -2.179449472 + -0.5 = -2.679449472 x = -2.679449472 Simplifying x = -2.679449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.679449472, -2.679449472}
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