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Simplifying 2x + -3 = x2 + -18x + -8 Reorder the terms: -3 + 2x = x2 + -18x + -8 Reorder the terms: -3 + 2x = -8 + -18x + x2 Solving -3 + 2x = -8 + -18x + x2 Solving for variable 'x'. Reorder the terms: -3 + 8 + 2x + 18x + -1x2 = -8 + -18x + x2 + 8 + 18x + -1x2 Combine like terms: -3 + 8 = 5 5 + 2x + 18x + -1x2 = -8 + -18x + x2 + 8 + 18x + -1x2 Combine like terms: 2x + 18x = 20x 5 + 20x + -1x2 = -8 + -18x + x2 + 8 + 18x + -1x2 Reorder the terms: 5 + 20x + -1x2 = -8 + 8 + -18x + 18x + x2 + -1x2 Combine like terms: -8 + 8 = 0 5 + 20x + -1x2 = 0 + -18x + 18x + x2 + -1x2 5 + 20x + -1x2 = -18x + 18x + x2 + -1x2 Combine like terms: -18x + 18x = 0 5 + 20x + -1x2 = 0 + x2 + -1x2 5 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -20x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -20x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -20x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -20x + x2 = 0 + 5 -20x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -20x + x2 = 5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 5 + 100 Reorder the terms: 100 + -20x + x2 = 5 + 100 Combine like terms: 5 + 100 = 105 100 + -20x + x2 = 105 Factor a perfect square on the left side: (x + -10)(x + -10) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + -10) equal to 10.246950766 and -10.246950766.Subproblem 1
x + -10 = 10.246950766 Simplifying x + -10 = 10.246950766 Reorder the terms: -10 + x = 10.246950766 Solving -10 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.246950766 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.246950766 + 10 x = 10.246950766 + 10 Combine like terms: 10.246950766 + 10 = 20.246950766 x = 20.246950766 Simplifying x = 20.246950766Subproblem 2
x + -10 = -10.246950766 Simplifying x + -10 = -10.246950766 Reorder the terms: -10 + x = -10.246950766 Solving -10 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.246950766 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.246950766 + 10 x = -10.246950766 + 10 Combine like terms: -10.246950766 + 10 = -0.246950766 x = -0.246950766 Simplifying x = -0.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.246950766, -0.246950766}
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