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Simplifying (x + -3)(x + -3) = 14 Reorder the terms: (-3 + x)(x + -3) = 14 Reorder the terms: (-3 + x)(-3 + x) = 14 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) = 14 ((-3 * -3 + x * -3) + x(-3 + x)) = 14 ((9 + -3x) + x(-3 + x)) = 14 (9 + -3x + (-3 * x + x * x)) = 14 (9 + -3x + (-3x + x2)) = 14 Combine like terms: -3x + -3x = -6x (9 + -6x + x2) = 14 Solving 9 + -6x + x2 = 14 Solving for variable 'x'. Reorder the terms: 9 + -14 + -6x + x2 = 14 + -14 Combine like terms: 9 + -14 = -5 -5 + -6x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -5 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -6x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -6x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6x + x2 = 0 + 5 -6x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6x + x2 = 5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 5 + 9 Reorder the terms: 9 + -6x + x2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6x + x2 = 14 Factor a perfect square on the left side: (x + -3)(x + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -3 = 3.741657387 Simplifying x + -3 = 3.741657387 Reorder the terms: -3 + x = 3.741657387 Solving -3 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.741657387 + 3 x = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 x = 6.741657387 Simplifying x = 6.741657387Subproblem 2
x + -3 = -3.741657387 Simplifying x + -3 = -3.741657387 Reorder the terms: -3 + x = -3.741657387 Solving -3 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.741657387 + 3 x = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 x = -0.741657387 Simplifying x = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.741657387, -0.741657387}
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