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Simplifying (x + -3)(x + -3) = 16 + -2x2 Reorder the terms: (-3 + x)(x + -3) = 16 + -2x2 Reorder the terms: (-3 + x)(-3 + x) = 16 + -2x2 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) = 16 + -2x2 ((-3 * -3 + x * -3) + x(-3 + x)) = 16 + -2x2 ((9 + -3x) + x(-3 + x)) = 16 + -2x2 (9 + -3x + (-3 * x + x * x)) = 16 + -2x2 (9 + -3x + (-3x + x2)) = 16 + -2x2 Combine like terms: -3x + -3x = -6x (9 + -6x + x2) = 16 + -2x2 Solving 9 + -6x + x2 = 16 + -2x2 Solving for variable 'x'. Reorder the terms: 9 + -16 + -6x + x2 + 2x2 = 16 + -2x2 + -16 + 2x2 Combine like terms: 9 + -16 = -7 -7 + -6x + x2 + 2x2 = 16 + -2x2 + -16 + 2x2 Combine like terms: x2 + 2x2 = 3x2 -7 + -6x + 3x2 = 16 + -2x2 + -16 + 2x2 Reorder the terms: -7 + -6x + 3x2 = 16 + -16 + -2x2 + 2x2 Combine like terms: 16 + -16 = 0 -7 + -6x + 3x2 = 0 + -2x2 + 2x2 -7 + -6x + 3x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -7 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -2x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -2x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 2.333333333 -2x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -2x + x2 = 2.333333333 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 = 2.333333333 + 1 Reorder the terms: 1 + -2x + x2 = 2.333333333 + 1 Combine like terms: 2.333333333 + 1 = 3.333333333 1 + -2x + x2 = 3.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.333333333 Calculate the square root of the right side: 1.825741858 Break this problem into two subproblems by setting (x + -1) equal to 1.825741858 and -1.825741858.Subproblem 1
x + -1 = 1.825741858 Simplifying x + -1 = 1.825741858 Reorder the terms: -1 + x = 1.825741858 Solving -1 + x = 1.825741858 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 = 1.825741858 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.825741858 + 1 x = 1.825741858 + 1 Combine like terms: 1.825741858 + 1 = 2.825741858 x = 2.825741858 Simplifying x = 2.825741858Subproblem 2
x + -1 = -1.825741858 Simplifying x + -1 = -1.825741858 Reorder the terms: -1 + x = -1.825741858 Solving -1 + x = -1.825741858 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 = -1.825741858 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.825741858 + 1 x = -1.825741858 + 1 Combine like terms: -1.825741858 + 1 = -0.825741858 x = -0.825741858 Simplifying x = -0.825741858Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.825741858, -0.825741858}
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