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Simplifying 4x2 + 33x + 15 = 0 Reorder the terms: 15 + 33x + 4x2 = 0 Solving 15 + 33x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 8.25x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 8.25x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 8.25x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 8.25x + x2 = 0 + -3.75 8.25x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 8.25x + x2 = -3.75 The x term is 8.25x. Take half its coefficient (4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. 8.25x + 17.015625 + x2 = -3.75 + 17.015625 Reorder the terms: 17.015625 + 8.25x + x2 = -3.75 + 17.015625 Combine like terms: -3.75 + 17.015625 = 13.265625 17.015625 + 8.25x + x2 = 13.265625 Factor a perfect square on the left side: (x + 4.125)(x + 4.125) = 13.265625 Calculate the square root of the right side: 3.642200571 Break this problem into two subproblems by setting (x + 4.125) equal to 3.642200571 and -3.642200571.Subproblem 1
x + 4.125 = 3.642200571 Simplifying x + 4.125 = 3.642200571 Reorder the terms: 4.125 + x = 3.642200571 Solving 4.125 + x = 3.642200571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.125' to each side of the equation. 4.125 + -4.125 + x = 3.642200571 + -4.125 Combine like terms: 4.125 + -4.125 = 0.000 0.000 + x = 3.642200571 + -4.125 x = 3.642200571 + -4.125 Combine like terms: 3.642200571 + -4.125 = -0.482799429 x = -0.482799429 Simplifying x = -0.482799429Subproblem 2
x + 4.125 = -3.642200571 Simplifying x + 4.125 = -3.642200571 Reorder the terms: 4.125 + x = -3.642200571 Solving 4.125 + x = -3.642200571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.125' to each side of the equation. 4.125 + -4.125 + x = -3.642200571 + -4.125 Combine like terms: 4.125 + -4.125 = 0.000 0.000 + x = -3.642200571 + -4.125 x = -3.642200571 + -4.125 Combine like terms: -3.642200571 + -4.125 = -7.767200571 x = -7.767200571 Simplifying x = -7.767200571Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.482799429, -7.767200571}
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