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Simplifying (x + -3x + -3) = (x + 1)(x + -1) + -20 Reorder the terms: (-3 + x + -3x) = (x + 1)(x + -1) + -20 Combine like terms: x + -3x = -2x (-3 + -2x) = (x + 1)(x + -1) + -20 Remove parenthesis around (-3 + -2x) -3 + -2x = (x + 1)(x + -1) + -20 Reorder the terms: -3 + -2x = (1 + x)(x + -1) + -20 Reorder the terms: -3 + -2x = (1 + x)(-1 + x) + -20 Multiply (1 + x) * (-1 + x) -3 + -2x = (1(-1 + x) + x(-1 + x)) + -20 -3 + -2x = ((-1 * 1 + x * 1) + x(-1 + x)) + -20 -3 + -2x = ((-1 + 1x) + x(-1 + x)) + -20 -3 + -2x = (-1 + 1x + (-1 * x + x * x)) + -20 -3 + -2x = (-1 + 1x + (-1x + x2)) + -20 Combine like terms: 1x + -1x = 0 -3 + -2x = (-1 + 0 + x2) + -20 -3 + -2x = (-1 + x2) + -20 Reorder the terms: -3 + -2x = -1 + -20 + x2 Combine like terms: -1 + -20 = -21 -3 + -2x = -21 + x2 Solving -3 + -2x = -21 + x2 Solving for variable 'x'. Reorder the terms: -3 + 21 + -2x + -1x2 = -21 + x2 + 21 + -1x2 Combine like terms: -3 + 21 = 18 18 + -2x + -1x2 = -21 + x2 + 21 + -1x2 Reorder the terms: 18 + -2x + -1x2 = -21 + 21 + x2 + -1x2 Combine like terms: -21 + 21 = 0 18 + -2x + -1x2 = 0 + x2 + -1x2 18 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + 2x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 2x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 2x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 2x + x2 = 0 + 18 2x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 2x + x2 = 18 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 = 18 + 1 Reorder the terms: 1 + 2x + x2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + 2x + x2 = 19 Factor a perfect square on the left side: (x + 1)(x + 1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 1) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 1 = 4.358898944 Simplifying x + 1 = 4.358898944 Reorder the terms: 1 + x = 4.358898944 Solving 1 + x = 4.358898944 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 = 4.358898944 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.358898944 + -1 x = 4.358898944 + -1 Combine like terms: 4.358898944 + -1 = 3.358898944 x = 3.358898944 Simplifying x = 3.358898944Subproblem 2
x + 1 = -4.358898944 Simplifying x + 1 = -4.358898944 Reorder the terms: 1 + x = -4.358898944 Solving 1 + x = -4.358898944 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 = -4.358898944 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.358898944 + -1 x = -4.358898944 + -1 Combine like terms: -4.358898944 + -1 = -5.358898944 x = -5.358898944 Simplifying x = -5.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.358898944, -5.358898944}
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