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Simplifying X2 + -12X + -676 = 0 Reorder the terms: -676 + -12X + X2 = 0 Solving -676 + -12X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '676' to each side of the equation. -676 + -12X + 676 + X2 = 0 + 676 Reorder the terms: -676 + 676 + -12X + X2 = 0 + 676 Combine like terms: -676 + 676 = 0 0 + -12X + X2 = 0 + 676 -12X + X2 = 0 + 676 Combine like terms: 0 + 676 = 676 -12X + X2 = 676 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 = 676 + 36 Reorder the terms: 36 + -12X + X2 = 676 + 36 Combine like terms: 676 + 36 = 712 36 + -12X + X2 = 712 Factor a perfect square on the left side: (X + -6)(X + -6) = 712 Calculate the square root of the right side: 26.683328128 Break this problem into two subproblems by setting (X + -6) equal to 26.683328128 and -26.683328128.Subproblem 1
X + -6 = 26.683328128 Simplifying X + -6 = 26.683328128 Reorder the terms: -6 + X = 26.683328128 Solving -6 + X = 26.683328128 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 = 26.683328128 + 6 Combine like terms: -6 + 6 = 0 0 + X = 26.683328128 + 6 X = 26.683328128 + 6 Combine like terms: 26.683328128 + 6 = 32.683328128 X = 32.683328128 Simplifying X = 32.683328128Subproblem 2
X + -6 = -26.683328128 Simplifying X + -6 = -26.683328128 Reorder the terms: -6 + X = -26.683328128 Solving -6 + X = -26.683328128 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 = -26.683328128 + 6 Combine like terms: -6 + 6 = 0 0 + X = -26.683328128 + 6 X = -26.683328128 + 6 Combine like terms: -26.683328128 + 6 = -20.683328128 X = -20.683328128 Simplifying X = -20.683328128Solution
The solution to the problem is based on the solutions from the subproblems. X = {32.683328128, -20.683328128}
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