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Simplifying x2 + -12x + -812 = 0 Reorder the terms: -812 + -12x + x2 = 0 Solving -812 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '812' to each side of the equation. -812 + -12x + 812 + x2 = 0 + 812 Reorder the terms: -812 + 812 + -12x + x2 = 0 + 812 Combine like terms: -812 + 812 = 0 0 + -12x + x2 = 0 + 812 -12x + x2 = 0 + 812 Combine like terms: 0 + 812 = 812 -12x + x2 = 812 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 = 812 + 36 Reorder the terms: 36 + -12x + x2 = 812 + 36 Combine like terms: 812 + 36 = 848 36 + -12x + x2 = 848 Factor a perfect square on the left side: (x + -6)(x + -6) = 848 Calculate the square root of the right side: 29.120439557 Break this problem into two subproblems by setting (x + -6) equal to 29.120439557 and -29.120439557.Subproblem 1
x + -6 = 29.120439557 Simplifying x + -6 = 29.120439557 Reorder the terms: -6 + x = 29.120439557 Solving -6 + x = 29.120439557 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 = 29.120439557 + 6 Combine like terms: -6 + 6 = 0 0 + x = 29.120439557 + 6 x = 29.120439557 + 6 Combine like terms: 29.120439557 + 6 = 35.120439557 x = 35.120439557 Simplifying x = 35.120439557Subproblem 2
x + -6 = -29.120439557 Simplifying x + -6 = -29.120439557 Reorder the terms: -6 + x = -29.120439557 Solving -6 + x = -29.120439557 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 = -29.120439557 + 6 Combine like terms: -6 + 6 = 0 0 + x = -29.120439557 + 6 x = -29.120439557 + 6 Combine like terms: -29.120439557 + 6 = -23.120439557 x = -23.120439557 Simplifying x = -23.120439557Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.120439557, -23.120439557}
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