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Simplifying (x + -3)(x + 3) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) Reorder the terms: (-3 + x)(x + 3) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) Reorder the terms: (-3 + x)(3 + x) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) Multiply (-3 + x) * (3 + x) (-3(3 + x) + x(3 + x)) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) ((3 * -3 + x * -3) + x(3 + x)) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) ((-9 + -3x) + x(3 + x)) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) (-9 + -3x + (3 * x + x * x)) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) (-9 + -3x + (3x + x2)) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) Combine like terms: -3x + 3x = 0 (-9 + 0 + x2) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) (-9 + x2) + -1(x + 3)(x + -3) = x + -2(x + 3)(x + -3) Reorder the terms: -9 + x2 + -1(3 + x)(x + -3) = x + -2(x + 3)(x + -3) Reorder the terms: -9 + x2 + -1(3 + x)(-3 + x) = x + -2(x + 3)(x + -3) Multiply (3 + x) * (-3 + x) -9 + x2 + -1(3(-3 + x) + x(-3 + x)) = x + -2(x + 3)(x + -3) -9 + x2 + -1((-3 * 3 + x * 3) + x(-3 + x)) = x + -2(x + 3)(x + -3) -9 + x2 + -1((-9 + 3x) + x(-3 + x)) = x + -2(x + 3)(x + -3) -9 + x2 + -1(-9 + 3x + (-3 * x + x * x)) = x + -2(x + 3)(x + -3) -9 + x2 + -1(-9 + 3x + (-3x + x2)) = x + -2(x + 3)(x + -3) Combine like terms: 3x + -3x = 0 -9 + x2 + -1(-9 + 0 + x2) = x + -2(x + 3)(x + -3) -9 + x2 + -1(-9 + x2) = x + -2(x + 3)(x + -3) -9 + x2 + (-9 * -1 + x2 * -1) = x + -2(x + 3)(x + -3) -9 + x2 + (9 + -1x2) = x + -2(x + 3)(x + -3) Reorder the terms: -9 + 9 + x2 + -1x2 = x + -2(x + 3)(x + -3) Combine like terms: -9 + 9 = 0 0 + x2 + -1x2 = x + -2(x + 3)(x + -3) x2 + -1x2 = x + -2(x + 3)(x + -3) Combine like terms: x2 + -1x2 = 0 0 = x + -2(x + 3)(x + -3) Reorder the terms: 0 = x + -2(3 + x)(x + -3) Reorder the terms: 0 = x + -2(3 + x)(-3 + x) Multiply (3 + x) * (-3 + x) 0 = x + -2(3(-3 + x) + x(-3 + x)) 0 = x + -2((-3 * 3 + x * 3) + x(-3 + x)) 0 = x + -2((-9 + 3x) + x(-3 + x)) 0 = x + -2(-9 + 3x + (-3 * x + x * x)) 0 = x + -2(-9 + 3x + (-3x + x2)) Combine like terms: 3x + -3x = 0 0 = x + -2(-9 + 0 + x2) 0 = x + -2(-9 + x2) 0 = x + (-9 * -2 + x2 * -2) 0 = x + (18 + -2x2) Reorder the terms: 0 = 18 + x + -2x2 Solving 0 = 18 + x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -18 = -18 -18 + -1x + 2x2 = 18 + x + -2x2 + -18 + -1x + 2x2 Reorder the terms: -18 + -1x + 2x2 = 18 + -18 + x + -1x + -2x2 + 2x2 Combine like terms: 18 + -18 = 0 -18 + -1x + 2x2 = 0 + x + -1x + -2x2 + 2x2 -18 + -1x + 2x2 = x + -1x + -2x2 + 2x2 Combine like terms: x + -1x = 0 -18 + -1x + 2x2 = 0 + -2x2 + 2x2 -18 + -1x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -18 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + -0.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.5x + x2 = 0 + 9 -0.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.5x + x2 = 9 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 = 9 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 9 + 0.0625 Combine like terms: 9 + 0.0625 = 9.0625 0.0625 + -0.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -0.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -0.25 = 3.010398645 Simplifying x + -0.25 = 3.010398645 Reorder the terms: -0.25 + x = 3.010398645 Solving -0.25 + x = 3.010398645 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 = 3.010398645 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.010398645 + 0.25 x = 3.010398645 + 0.25 Combine like terms: 3.010398645 + 0.25 = 3.260398645 x = 3.260398645 Simplifying x = 3.260398645Subproblem 2
x + -0.25 = -3.010398645 Simplifying x + -0.25 = -3.010398645 Reorder the terms: -0.25 + x = -3.010398645 Solving -0.25 + x = -3.010398645 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 = -3.010398645 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.010398645 + 0.25 x = -3.010398645 + 0.25 Combine like terms: -3.010398645 + 0.25 = -2.760398645 x = -2.760398645 Simplifying x = -2.760398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.260398645, -2.760398645}
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