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Simplifying 3 = -16x2 + 144x Reorder the terms: 3 = 144x + -16x2 Solving 3 = 144x + -16x2 Solving for variable 'x'. Reorder the terms: 3 + -144x + 16x2 = 144x + -144x + -16x2 + 16x2 Combine like terms: 144x + -144x = 0 3 + -144x + 16x2 = 0 + -16x2 + 16x2 3 + -144x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 3 + -144x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + -9x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -9x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -9x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -9x + x2 = 0 + -0.1875 -9x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -9x + x2 = -0.1875 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -0.1875 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -0.1875 + 20.25 Combine like terms: -0.1875 + 20.25 = 20.0625 20.25 + -9x + x2 = 20.0625 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + -4.5) equal to 4.479118217 and -4.479118217.Subproblem 1
x + -4.5 = 4.479118217 Simplifying x + -4.5 = 4.479118217 Reorder the terms: -4.5 + x = 4.479118217 Solving -4.5 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.479118217 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.479118217 + 4.5 x = 4.479118217 + 4.5 Combine like terms: 4.479118217 + 4.5 = 8.979118217 x = 8.979118217 Simplifying x = 8.979118217Subproblem 2
x + -4.5 = -4.479118217 Simplifying x + -4.5 = -4.479118217 Reorder the terms: -4.5 + x = -4.479118217 Solving -4.5 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.479118217 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.479118217 + 4.5 x = -4.479118217 + 4.5 Combine like terms: -4.479118217 + 4.5 = 0.020881783 x = 0.020881783 Simplifying x = 0.020881783Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.979118217, 0.020881783}
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