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Simplifying (x + -6)(x + -6) = 7 Reorder the terms: (-6 + x)(x + -6) = 7 Reorder the terms: (-6 + x)(-6 + x) = 7 Multiply (-6 + x) * (-6 + x) (-6(-6 + x) + x(-6 + x)) = 7 ((-6 * -6 + x * -6) + x(-6 + x)) = 7 ((36 + -6x) + x(-6 + x)) = 7 (36 + -6x + (-6 * x + x * x)) = 7 (36 + -6x + (-6x + x2)) = 7 Combine like terms: -6x + -6x = -12x (36 + -12x + x2) = 7 Solving 36 + -12x + x2 = 7 Solving for variable 'x'. Reorder the terms: 36 + -7 + -12x + x2 = 7 + -7 Combine like terms: 36 + -7 = 29 29 + -12x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 29 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -12x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + -12x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -12x + x2 = 0 + -29 -12x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 -12x + x2 = -29 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -29 + 36 Reorder the terms: 36 + -12x + x2 = -29 + 36 Combine like terms: -29 + 36 = 7 36 + -12x + x2 = 7 Factor a perfect square on the left side: (x + -6)(x + -6) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -6) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -6 = 2.645751311 Simplifying x + -6 = 2.645751311 Reorder the terms: -6 + x = 2.645751311 Solving -6 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 2.645751311 + 6 Combine like terms: -6 + 6 = 0 0 + x = 2.645751311 + 6 x = 2.645751311 + 6 Combine like terms: 2.645751311 + 6 = 8.645751311 x = 8.645751311 Simplifying x = 8.645751311Subproblem 2
x + -6 = -2.645751311 Simplifying x + -6 = -2.645751311 Reorder the terms: -6 + x = -2.645751311 Solving -6 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -2.645751311 + 6 Combine like terms: -6 + 6 = 0 0 + x = -2.645751311 + 6 x = -2.645751311 + 6 Combine like terms: -2.645751311 + 6 = 3.354248689 x = 3.354248689 Simplifying x = 3.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.645751311, 3.354248689}
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