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Simplifying 27 + -1(x + -6)(x + -6) = 0 Reorder the terms: 27 + -1(-6 + x)(x + -6) = 0 Reorder the terms: 27 + -1(-6 + x)(-6 + x) = 0 Multiply (-6 + x) * (-6 + x) 27 + -1(-6(-6 + x) + x(-6 + x)) = 0 27 + -1((-6 * -6 + x * -6) + x(-6 + x)) = 0 27 + -1((36 + -6x) + x(-6 + x)) = 0 27 + -1(36 + -6x + (-6 * x + x * x)) = 0 27 + -1(36 + -6x + (-6x + x2)) = 0 Combine like terms: -6x + -6x = -12x 27 + -1(36 + -12x + x2) = 0 27 + (36 * -1 + -12x * -1 + x2 * -1) = 0 27 + (-36 + 12x + -1x2) = 0 Combine like terms: 27 + -36 = -9 -9 + 12x + -1x2 = 0 Solving -9 + 12x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -12x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -12x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -12x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -12x + x2 = 0 + -9 -12x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -12x + x2 = -9 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 = -9 + 36 Reorder the terms: 36 + -12x + x2 = -9 + 36 Combine like terms: -9 + 36 = 27 36 + -12x + x2 = 27 Factor a perfect square on the left side: (x + -6)(x + -6) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -6) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -6 = 5.196152423 Simplifying x + -6 = 5.196152423 Reorder the terms: -6 + x = 5.196152423 Solving -6 + x = 5.196152423 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 = 5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.196152423 + 6 x = 5.196152423 + 6 Combine like terms: 5.196152423 + 6 = 11.196152423 x = 11.196152423 Simplifying x = 11.196152423Subproblem 2
x + -6 = -5.196152423 Simplifying x + -6 = -5.196152423 Reorder the terms: -6 + x = -5.196152423 Solving -6 + x = -5.196152423 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 = -5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.196152423 + 6 x = -5.196152423 + 6 Combine like terms: -5.196152423 + 6 = 0.803847577 x = 0.803847577 Simplifying x = 0.803847577Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.196152423, 0.803847577}
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