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Simplifying x2 + -12x + -340 = 0 Reorder the terms: -340 + -12x + x2 = 0 Solving -340 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '340' to each side of the equation. -340 + -12x + 340 + x2 = 0 + 340 Reorder the terms: -340 + 340 + -12x + x2 = 0 + 340 Combine like terms: -340 + 340 = 0 0 + -12x + x2 = 0 + 340 -12x + x2 = 0 + 340 Combine like terms: 0 + 340 = 340 -12x + x2 = 340 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 = 340 + 36 Reorder the terms: 36 + -12x + x2 = 340 + 36 Combine like terms: 340 + 36 = 376 36 + -12x + x2 = 376 Factor a perfect square on the left side: (x + -6)(x + -6) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (x + -6) equal to 19.39071943 and -19.39071943.Subproblem 1
x + -6 = 19.39071943 Simplifying x + -6 = 19.39071943 Reorder the terms: -6 + x = 19.39071943 Solving -6 + x = 19.39071943 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 = 19.39071943 + 6 Combine like terms: -6 + 6 = 0 0 + x = 19.39071943 + 6 x = 19.39071943 + 6 Combine like terms: 19.39071943 + 6 = 25.39071943 x = 25.39071943 Simplifying x = 25.39071943Subproblem 2
x + -6 = -19.39071943 Simplifying x + -6 = -19.39071943 Reorder the terms: -6 + x = -19.39071943 Solving -6 + x = -19.39071943 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 = -19.39071943 + 6 Combine like terms: -6 + 6 = 0 0 + x = -19.39071943 + 6 x = -19.39071943 + 6 Combine like terms: -19.39071943 + 6 = -13.39071943 x = -13.39071943 Simplifying x = -13.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.39071943, -13.39071943}
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