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Simplifying x2 + -12x + -62 = 0 Reorder the terms: -62 + -12x + x2 = 0 Solving -62 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + -12x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -12x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -12x + x2 = 0 + 62 -12x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -12x + x2 = 62 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 = 62 + 36 Reorder the terms: 36 + -12x + x2 = 62 + 36 Combine like terms: 62 + 36 = 98 36 + -12x + x2 = 98 Factor a perfect square on the left side: (x + -6)(x + -6) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -6) equal to 9.899494937 and -9.899494937.Subproblem 1
x + -6 = 9.899494937 Simplifying x + -6 = 9.899494937 Reorder the terms: -6 + x = 9.899494937 Solving -6 + x = 9.899494937 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 = 9.899494937 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.899494937 + 6 x = 9.899494937 + 6 Combine like terms: 9.899494937 + 6 = 15.899494937 x = 15.899494937 Simplifying x = 15.899494937Subproblem 2
x + -6 = -9.899494937 Simplifying x + -6 = -9.899494937 Reorder the terms: -6 + x = -9.899494937 Solving -6 + x = -9.899494937 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 = -9.899494937 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.899494937 + 6 x = -9.899494937 + 6 Combine like terms: -9.899494937 + 6 = -3.899494937 x = -3.899494937 Simplifying x = -3.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.899494937, -3.899494937}
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