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Simplifying 16x + 8 = x2 + -2x + -3 Reorder the terms: 8 + 16x = x2 + -2x + -3 Reorder the terms: 8 + 16x = -3 + -2x + x2 Solving 8 + 16x = -3 + -2x + x2 Solving for variable 'x'. Reorder the terms: 8 + 3 + 16x + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: 8 + 3 = 11 11 + 16x + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: 16x + 2x = 18x 11 + 18x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Reorder the terms: 11 + 18x + -1x2 = -3 + 3 + -2x + 2x + x2 + -1x2 Combine like terms: -3 + 3 = 0 11 + 18x + -1x2 = 0 + -2x + 2x + x2 + -1x2 11 + 18x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 11 + 18x + -1x2 = 0 + x2 + -1x2 11 + 18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -18x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -18x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -18x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -18x + x2 = 0 + 11 -18x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -18x + x2 = 11 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 11 + 81 Reorder the terms: 81 + -18x + x2 = 11 + 81 Combine like terms: 11 + 81 = 92 81 + -18x + x2 = 92 Factor a perfect square on the left side: (x + -9)(x + -9) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (x + -9) equal to 9.591663047 and -9.591663047.Subproblem 1
x + -9 = 9.591663047 Simplifying x + -9 = 9.591663047 Reorder the terms: -9 + x = 9.591663047 Solving -9 + x = 9.591663047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.591663047 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.591663047 + 9 x = 9.591663047 + 9 Combine like terms: 9.591663047 + 9 = 18.591663047 x = 18.591663047 Simplifying x = 18.591663047Subproblem 2
x + -9 = -9.591663047 Simplifying x + -9 = -9.591663047 Reorder the terms: -9 + x = -9.591663047 Solving -9 + x = -9.591663047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.591663047 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.591663047 + 9 x = -9.591663047 + 9 Combine like terms: -9.591663047 + 9 = -0.591663047 x = -0.591663047 Simplifying x = -0.591663047Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.591663047, -0.591663047}
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