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Simplifying x2 + -12x = 256 Reorder the terms: -12x + x2 = 256 Solving -12x + x2 = 256 Solving for variable 'x'. Reorder the terms: -256 + -12x + x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + -12x + x2 = 0 Begin completing the square. 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 = 23.088007491 x = 23.088007491 Simplifying x = 23.088007491Subproblem 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 = -11.088007491 x = -11.088007491 Simplifying x = -11.088007491Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.088007491, -11.088007491}
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