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Simplifying (x + -3)(x + 3) = (x + -3x + -3) Reorder the terms: (-3 + x)(x + 3) = (x + -3x + -3) Reorder the terms: (-3 + x)(3 + x) = (x + -3x + -3) Multiply (-3 + x) * (3 + x) (-3(3 + x) + x(3 + x)) = (x + -3x + -3) ((3 * -3 + x * -3) + x(3 + x)) = (x + -3x + -3) ((-9 + -3x) + x(3 + x)) = (x + -3x + -3) (-9 + -3x + (3 * x + x * x)) = (x + -3x + -3) (-9 + -3x + (3x + x2)) = (x + -3x + -3) Combine like terms: -3x + 3x = 0 (-9 + 0 + x2) = (x + -3x + -3) (-9 + x2) = (x + -3x + -3) Reorder the terms: -9 + x2 = (-3 + x + -3x) Combine like terms: x + -3x = -2x -9 + x2 = (-3 + -2x) Remove parenthesis around (-3 + -2x) -9 + x2 = -3 + -2x Solving -9 + x2 = -3 + -2x Solving for variable 'x'. Reorder the terms: -9 + 3 + 2x + x2 = -3 + -2x + 3 + 2x Combine like terms: -9 + 3 = -6 -6 + 2x + x2 = -3 + -2x + 3 + 2x Reorder the terms: -6 + 2x + x2 = -3 + 3 + -2x + 2x Combine like terms: -3 + 3 = 0 -6 + 2x + x2 = 0 + -2x + 2x -6 + 2x + x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -6 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 2x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 2x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2x + x2 = 0 + 6 2x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 2x + x2 = 6 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 = 6 + 1 Reorder the terms: 1 + 2x + x2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + 2x + x2 = 7 Factor a perfect square on the left side: (x + 1)(x + 1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 1) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 1 = 2.645751311 Simplifying x + 1 = 2.645751311 Reorder the terms: 1 + x = 2.645751311 Solving 1 + x = 2.645751311 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 = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.645751311 + -1 x = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 x = 1.645751311 Simplifying x = 1.645751311Subproblem 2
x + 1 = -2.645751311 Simplifying x + 1 = -2.645751311 Reorder the terms: 1 + x = -2.645751311 Solving 1 + x = -2.645751311 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 = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.645751311 + -1 x = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 x = -3.645751311 Simplifying x = -3.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.645751311, -3.645751311}
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