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Simplifying x2 + 12x + -50 = 0 Reorder the terms: -50 + 12x + x2 = 0 Solving -50 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 12x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 12x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 12x + x2 = 0 + 50 12x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 12x + x2 = 50 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 = 50 + 36 Reorder the terms: 36 + 12x + x2 = 50 + 36 Combine like terms: 50 + 36 = 86 36 + 12x + x2 = 86 Factor a perfect square on the left side: (x + 6)(x + 6) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 6) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 6 = 9.273618495 Simplifying x + 6 = 9.273618495 Reorder the terms: 6 + x = 9.273618495 Solving 6 + x = 9.273618495 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 = 9.273618495 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.273618495 + -6 x = 9.273618495 + -6 Combine like terms: 9.273618495 + -6 = 3.273618495 x = 3.273618495 Simplifying x = 3.273618495Subproblem 2
x + 6 = -9.273618495 Simplifying x + 6 = -9.273618495 Reorder the terms: 6 + x = -9.273618495 Solving 6 + x = -9.273618495 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 = -9.273618495 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.273618495 + -6 x = -9.273618495 + -6 Combine like terms: -9.273618495 + -6 = -15.273618495 x = -15.273618495 Simplifying x = -15.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.273618495, -15.273618495}
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