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Simplifying (x + -3)(x + -3) = 45 Reorder the terms: (-3 + x)(x + -3) = 45 Reorder the terms: (-3 + x)(-3 + x) = 45 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) = 45 ((-3 * -3 + x * -3) + x(-3 + x)) = 45 ((9 + -3x) + x(-3 + x)) = 45 (9 + -3x + (-3 * x + x * x)) = 45 (9 + -3x + (-3x + x2)) = 45 Combine like terms: -3x + -3x = -6x (9 + -6x + x2) = 45 Solving 9 + -6x + x2 = 45 Solving for variable 'x'. Reorder the terms: 9 + -45 + -6x + x2 = 45 + -45 Combine like terms: 9 + -45 = -36 -36 + -6x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -36 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -6x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -6x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -6x + x2 = 0 + 36 -6x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -6x + x2 = 36 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 = 36 + 9 Reorder the terms: 9 + -6x + x2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + -6x + x2 = 45 Factor a perfect square on the left side: (x + -3)(x + -3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -3) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -3 = 6.708203933 Simplifying x + -3 = 6.708203933 Reorder the terms: -3 + x = 6.708203933 Solving -3 + x = 6.708203933 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 = 6.708203933 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.708203933 + 3 x = 6.708203933 + 3 Combine like terms: 6.708203933 + 3 = 9.708203933 x = 9.708203933 Simplifying x = 9.708203933Subproblem 2
x + -3 = -6.708203933 Simplifying x + -3 = -6.708203933 Reorder the terms: -3 + x = -6.708203933 Solving -3 + x = -6.708203933 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 = -6.708203933 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.708203933 + 3 x = -6.708203933 + 3 Combine like terms: -6.708203933 + 3 = -3.708203933 x = -3.708203933 Simplifying x = -3.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.708203933, -3.708203933}
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