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Simplifying x2 = 12x + 56 Reorder the terms: x2 = 56 + 12x Solving x2 = 56 + 12x Solving for variable 'x'. Reorder the terms: -56 + -12x + x2 = 56 + 12x + -56 + -12x Reorder the terms: -56 + -12x + x2 = 56 + -56 + 12x + -12x Combine like terms: 56 + -56 = 0 -56 + -12x + x2 = 0 + 12x + -12x -56 + -12x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -56 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -12x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -12x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -12x + x2 = 0 + 56 -12x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -12x + x2 = 56 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 = 56 + 36 Reorder the terms: 36 + -12x + x2 = 56 + 36 Combine like terms: 56 + 36 = 92 36 + -12x + x2 = 92 Factor a perfect square on the left side: (x + -6)(x + -6) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (x + -6) equal to 9.591663047 and -9.591663047.Subproblem 1
x + -6 = 9.591663047 Simplifying x + -6 = 9.591663047 Reorder the terms: -6 + x = 9.591663047 Solving -6 + x = 9.591663047 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 = 9.591663047 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.591663047 + 6 x = 9.591663047 + 6 Combine like terms: 9.591663047 + 6 = 15.591663047 x = 15.591663047 Simplifying x = 15.591663047Subproblem 2
x + -6 = -9.591663047 Simplifying x + -6 = -9.591663047 Reorder the terms: -6 + x = -9.591663047 Solving -6 + x = -9.591663047 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 = -9.591663047 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.591663047 + 6 x = -9.591663047 + 6 Combine like terms: -9.591663047 + 6 = -3.591663047 x = -3.591663047 Simplifying x = -3.591663047Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.591663047, -3.591663047}
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