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Simplifying x = (x + 2)(x + -2) Reorder the terms: x = (2 + x)(x + -2) Reorder the terms: x = (2 + x)(-2 + x) Multiply (2 + x) * (-2 + x) x = (2(-2 + x) + x(-2 + x)) x = ((-2 * 2 + x * 2) + x(-2 + x)) x = ((-4 + 2x) + x(-2 + x)) x = (-4 + 2x + (-2 * x + x * x)) x = (-4 + 2x + (-2x + x2)) Combine like terms: 2x + -2x = 0 x = (-4 + 0 + x2) x = (-4 + x2) Solving x = -4 + x2 Solving for variable 'x'. Reorder the terms: 4 + x + -1x2 = -4 + x2 + 4 + -1x2 Reorder the terms: 4 + x + -1x2 = -4 + 4 + x2 + -1x2 Combine like terms: -4 + 4 = 0 4 + x + -1x2 = 0 + x2 + -1x2 4 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -1x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x + x2 = 0 + 4 -1x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1x + x2 = 4 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. -1x + 0.25 + x2 = 4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + -1x + x2 = 4.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 0.5 = 2.061552813 Simplifying x + 0.5 = 2.061552813 Reorder the terms: 0.5 + x = 2.061552813 Solving 0.5 + x = 2.061552813 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 = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.061552813 + -0.5 x = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 x = 1.561552813 Simplifying x = 1.561552813Subproblem 2
x + 0.5 = -2.061552813 Simplifying x + 0.5 = -2.061552813 Reorder the terms: 0.5 + x = -2.061552813 Solving 0.5 + x = -2.061552813 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 = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.061552813 + -0.5 x = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 x = -2.561552813 Simplifying x = -2.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.561552813, -2.561552813}
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