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Simplifying 12x + 50 = x2 Reorder the terms: 50 + 12x = x2 Solving 50 + 12x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 50 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -12x + x2 = 0 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 = 15.273618495 x = 15.273618495 Simplifying x = 15.273618495Subproblem 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 = -3.273618495 x = -3.273618495 Simplifying x = -3.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.273618495, -3.273618495}
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