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Simplifying 12x2 + -24x = x + 8 Reorder the terms: -24x + 12x2 = x + 8 Reorder the terms: -24x + 12x2 = 8 + x Solving -24x + 12x2 = 8 + x Solving for variable 'x'. Reorder the terms: -8 + -24x + -1x + 12x2 = 8 + x + -8 + -1x Combine like terms: -24x + -1x = -25x -8 + -25x + 12x2 = 8 + x + -8 + -1x Reorder the terms: -8 + -25x + 12x2 = 8 + -8 + x + -1x Combine like terms: 8 + -8 = 0 -8 + -25x + 12x2 = 0 + x + -1x -8 + -25x + 12x2 = x + -1x Combine like terms: x + -1x = 0 -8 + -25x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.6666666667 + -2.083333333x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -2.083333333x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -2.083333333x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -2.083333333x + x2 = 0 + 0.6666666667 -2.083333333x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -2.083333333x + x2 = 0.6666666667 The x term is -2.083333333x. Take half its coefficient (-1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. -2.083333333x + 1.085069445 + x2 = 0.6666666667 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333x + x2 = 0.6666666667 + 1.085069445 Combine like terms: 0.6666666667 + 1.085069445 = 1.7517361117 1.085069445 + -2.083333333x + x2 = 1.7517361117 Factor a perfect square on the left side: (x + -1.041666667)(x + -1.041666667) = 1.7517361117 Calculate the square root of the right side: 1.323531681 Break this problem into two subproblems by setting (x + -1.041666667) equal to 1.323531681 and -1.323531681.Subproblem 1
x + -1.041666667 = 1.323531681 Simplifying x + -1.041666667 = 1.323531681 Reorder the terms: -1.041666667 + x = 1.323531681 Solving -1.041666667 + x = 1.323531681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = 1.323531681 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = 1.323531681 + 1.041666667 x = 1.323531681 + 1.041666667 Combine like terms: 1.323531681 + 1.041666667 = 2.365198348 x = 2.365198348 Simplifying x = 2.365198348Subproblem 2
x + -1.041666667 = -1.323531681 Simplifying x + -1.041666667 = -1.323531681 Reorder the terms: -1.041666667 + x = -1.323531681 Solving -1.041666667 + x = -1.323531681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = -1.323531681 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = -1.323531681 + 1.041666667 x = -1.323531681 + 1.041666667 Combine like terms: -1.323531681 + 1.041666667 = -0.281865014 x = -0.281865014 Simplifying x = -0.281865014Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.365198348, -0.281865014}
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