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Simplifying 0 = -16x2 + 159x + -45 Reorder the terms: 0 = -45 + 159x + -16x2 Solving 0 = -45 + 159x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 45 = 45 45 + -159x + 16x2 = -45 + 159x + -16x2 + 45 + -159x + 16x2 Reorder the terms: 45 + -159x + 16x2 = -45 + 45 + 159x + -159x + -16x2 + 16x2 Combine like terms: -45 + 45 = 0 45 + -159x + 16x2 = 0 + 159x + -159x + -16x2 + 16x2 45 + -159x + 16x2 = 159x + -159x + -16x2 + 16x2 Combine like terms: 159x + -159x = 0 45 + -159x + 16x2 = 0 + -16x2 + 16x2 45 + -159x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 45 + -159x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.8125 + -9.9375x + x2 = 0 Move the constant term to the right: Add '-2.8125' to each side of the equation. 2.8125 + -9.9375x + -2.8125 + x2 = 0 + -2.8125 Reorder the terms: 2.8125 + -2.8125 + -9.9375x + x2 = 0 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + -9.9375x + x2 = 0 + -2.8125 -9.9375x + x2 = 0 + -2.8125 Combine like terms: 0 + -2.8125 = -2.8125 -9.9375x + x2 = -2.8125 The x term is -9.9375x. Take half its coefficient (-4.96875). Square it (24.68847656) and add it to both sides. Add '24.68847656' to each side of the equation. -9.9375x + 24.68847656 + x2 = -2.8125 + 24.68847656 Reorder the terms: 24.68847656 + -9.9375x + x2 = -2.8125 + 24.68847656 Combine like terms: -2.8125 + 24.68847656 = 21.87597656 24.68847656 + -9.9375x + x2 = 21.87597656 Factor a perfect square on the left side: (x + -4.96875)(x + -4.96875) = 21.87597656 Calculate the square root of the right side: 4.677176131 Break this problem into two subproblems by setting (x + -4.96875) equal to 4.677176131 and -4.677176131.Subproblem 1
x + -4.96875 = 4.677176131 Simplifying x + -4.96875 = 4.677176131 Reorder the terms: -4.96875 + x = 4.677176131 Solving -4.96875 + x = 4.677176131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.96875' to each side of the equation. -4.96875 + 4.96875 + x = 4.677176131 + 4.96875 Combine like terms: -4.96875 + 4.96875 = 0.00000 0.00000 + x = 4.677176131 + 4.96875 x = 4.677176131 + 4.96875 Combine like terms: 4.677176131 + 4.96875 = 9.645926131 x = 9.645926131 Simplifying x = 9.645926131Subproblem 2
x + -4.96875 = -4.677176131 Simplifying x + -4.96875 = -4.677176131 Reorder the terms: -4.96875 + x = -4.677176131 Solving -4.96875 + x = -4.677176131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.96875' to each side of the equation. -4.96875 + 4.96875 + x = -4.677176131 + 4.96875 Combine like terms: -4.96875 + 4.96875 = 0.00000 0.00000 + x = -4.677176131 + 4.96875 x = -4.677176131 + 4.96875 Combine like terms: -4.677176131 + 4.96875 = 0.291573869 x = 0.291573869 Simplifying x = 0.291573869Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.645926131, 0.291573869}
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