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Simplifying 16x2 + 180x + 147 = 0 Reorder the terms: 147 + 180x + 16x2 = 0 Solving 147 + 180x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 9.1875 + 11.25x + x2 = 0 Move the constant term to the right: Add '-9.1875' to each side of the equation. 9.1875 + 11.25x + -9.1875 + x2 = 0 + -9.1875 Reorder the terms: 9.1875 + -9.1875 + 11.25x + x2 = 0 + -9.1875 Combine like terms: 9.1875 + -9.1875 = 0.0000 0.0000 + 11.25x + x2 = 0 + -9.1875 11.25x + x2 = 0 + -9.1875 Combine like terms: 0 + -9.1875 = -9.1875 11.25x + x2 = -9.1875 The x term is 11.25x. Take half its coefficient (5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. 11.25x + 31.640625 + x2 = -9.1875 + 31.640625 Reorder the terms: 31.640625 + 11.25x + x2 = -9.1875 + 31.640625 Combine like terms: -9.1875 + 31.640625 = 22.453125 31.640625 + 11.25x + x2 = 22.453125 Factor a perfect square on the left side: (x + 5.625)(x + 5.625) = 22.453125 Calculate the square root of the right side: 4.738472855 Break this problem into two subproblems by setting (x + 5.625) equal to 4.738472855 and -4.738472855.Subproblem 1
x + 5.625 = 4.738472855 Simplifying x + 5.625 = 4.738472855 Reorder the terms: 5.625 + x = 4.738472855 Solving 5.625 + x = 4.738472855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = 4.738472855 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = 4.738472855 + -5.625 x = 4.738472855 + -5.625 Combine like terms: 4.738472855 + -5.625 = -0.886527145 x = -0.886527145 Simplifying x = -0.886527145Subproblem 2
x + 5.625 = -4.738472855 Simplifying x + 5.625 = -4.738472855 Reorder the terms: 5.625 + x = -4.738472855 Solving 5.625 + x = -4.738472855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = -4.738472855 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = -4.738472855 + -5.625 x = -4.738472855 + -5.625 Combine like terms: -4.738472855 + -5.625 = -10.363472855 x = -10.363472855 Simplifying x = -10.363472855Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.886527145, -10.363472855}
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