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Simplifying x2 + -12x + -6 = 52 Reorder the terms: -6 + -12x + x2 = 52 Solving -6 + -12x + x2 = 52 Solving for variable 'x'. Reorder the terms: -6 + -52 + -12x + x2 = 52 + -52 Combine like terms: -6 + -52 = -58 -58 + -12x + x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -58 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -12x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + -12x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -12x + x2 = 0 + 58 -12x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 -12x + x2 = 58 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 = 58 + 36 Reorder the terms: 36 + -12x + x2 = 58 + 36 Combine like terms: 58 + 36 = 94 36 + -12x + x2 = 94 Factor a perfect square on the left side: (x + -6)(x + -6) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + -6) equal to 9.695359715 and -9.695359715.Subproblem 1
x + -6 = 9.695359715 Simplifying x + -6 = 9.695359715 Reorder the terms: -6 + x = 9.695359715 Solving -6 + x = 9.695359715 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 = 9.695359715 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.695359715 + 6 x = 9.695359715 + 6 Combine like terms: 9.695359715 + 6 = 15.695359715 x = 15.695359715 Simplifying x = 15.695359715Subproblem 2
x + -6 = -9.695359715 Simplifying x + -6 = -9.695359715 Reorder the terms: -6 + x = -9.695359715 Solving -6 + x = -9.695359715 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 = -9.695359715 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.695359715 + 6 x = -9.695359715 + 6 Combine like terms: -9.695359715 + 6 = -3.695359715 x = -3.695359715 Simplifying x = -3.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.695359715, -3.695359715}
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