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Simplifying 256 = x2 + 12x Reorder the terms: 256 = 12x + x2 Solving 256 = 12x + x2 Solving for variable 'x'. Reorder the terms: 256 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 256 + -12x + -1x2 = 0 + x2 + -1x2 256 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 256 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -256 + 12x + x2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + 12x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 12x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 12x + x2 = 0 + 256 12x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 12x + x2 = 256 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 = 256 + 36 Reorder the terms: 36 + 12x + x2 = 256 + 36 Combine like terms: 256 + 36 = 292 36 + 12x + x2 = 292 Factor a perfect square on the left side: (x + 6)(x + 6) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x + 6) equal to 17.088007491 and -17.088007491.Subproblem 1
x + 6 = 17.088007491 Simplifying x + 6 = 17.088007491 Reorder the terms: 6 + x = 17.088007491 Solving 6 + x = 17.088007491 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 = 17.088007491 + -6 Combine like terms: 6 + -6 = 0 0 + x = 17.088007491 + -6 x = 17.088007491 + -6 Combine like terms: 17.088007491 + -6 = 11.088007491 x = 11.088007491 Simplifying x = 11.088007491Subproblem 2
x + 6 = -17.088007491 Simplifying x + 6 = -17.088007491 Reorder the terms: 6 + x = -17.088007491 Solving 6 + x = -17.088007491 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 = -17.088007491 + -6 Combine like terms: 6 + -6 = 0 0 + x = -17.088007491 + -6 x = -17.088007491 + -6 Combine like terms: -17.088007491 + -6 = -23.088007491 x = -23.088007491 Simplifying x = -23.088007491Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.088007491, -23.088007491}
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