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Simplifying x2 + -12x = 676 Reorder the terms: -12x + x2 = 676 Solving -12x + x2 = 676 Solving for variable 'x'. Reorder the terms: -676 + -12x + x2 = 676 + -676 Combine like terms: 676 + -676 = 0 -676 + -12x + x2 = 0 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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