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Simplifying -16x2 + 108x + 3 = 0 Reorder the terms: 3 + 108x + -16x2 = 0 Solving 3 + 108x + -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'. -0.1875 + -6.75x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -6.75x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -6.75x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -6.75x + x2 = 0 + 0.1875 -6.75x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -6.75x + x2 = 0.1875 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = 0.1875 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = 0.1875 + 11.390625 Combine like terms: 0.1875 + 11.390625 = 11.578125 11.390625 + -6.75x + x2 = 11.578125 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 11.578125 Calculate the square root of the right side: 3.402664397 Break this problem into two subproblems by setting (x + -3.375) equal to 3.402664397 and -3.402664397.Subproblem 1
x + -3.375 = 3.402664397 Simplifying x + -3.375 = 3.402664397 Reorder the terms: -3.375 + x = 3.402664397 Solving -3.375 + x = 3.402664397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 3.402664397 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 3.402664397 + 3.375 x = 3.402664397 + 3.375 Combine like terms: 3.402664397 + 3.375 = 6.777664397 x = 6.777664397 Simplifying x = 6.777664397Subproblem 2
x + -3.375 = -3.402664397 Simplifying x + -3.375 = -3.402664397 Reorder the terms: -3.375 + x = -3.402664397 Solving -3.375 + x = -3.402664397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -3.402664397 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -3.402664397 + 3.375 x = -3.402664397 + 3.375 Combine like terms: -3.402664397 + 3.375 = -0.027664397 x = -0.027664397 Simplifying x = -0.027664397Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.777664397, -0.027664397}
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