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Simplifying 0 = 60 + 12x + -1x2 Solving 0 = 60 + 12x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + -12x + x2 = 60 + 12x + -1x2 + -60 + -12x + x2 Reorder the terms: -60 + -12x + x2 = 60 + -60 + 12x + -12x + -1x2 + x2 Combine like terms: 60 + -60 = 0 -60 + -12x + x2 = 0 + 12x + -12x + -1x2 + x2 -60 + -12x + x2 = 12x + -12x + -1x2 + x2 Combine like terms: 12x + -12x = 0 -60 + -12x + x2 = 0 + -1x2 + x2 -60 + -12x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -60 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -12x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -12x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -12x + x2 = 0 + 60 -12x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -12x + x2 = 60 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 = 60 + 36 Reorder the terms: 36 + -12x + x2 = 60 + 36 Combine like terms: 60 + 36 = 96 36 + -12x + x2 = 96 Factor a perfect square on the left side: (x + -6)(x + -6) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + -6) equal to 9.797958971 and -9.797958971.Subproblem 1
x + -6 = 9.797958971 Simplifying x + -6 = 9.797958971 Reorder the terms: -6 + x = 9.797958971 Solving -6 + x = 9.797958971 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 = 9.797958971 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.797958971 + 6 x = 9.797958971 + 6 Combine like terms: 9.797958971 + 6 = 15.797958971 x = 15.797958971 Simplifying x = 15.797958971Subproblem 2
x + -6 = -9.797958971 Simplifying x + -6 = -9.797958971 Reorder the terms: -6 + x = -9.797958971 Solving -6 + x = -9.797958971 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 = -9.797958971 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.797958971 + 6 x = -9.797958971 + 6 Combine like terms: -9.797958971 + 6 = -3.797958971 x = -3.797958971 Simplifying x = -3.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.797958971, -3.797958971}
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