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Simplifying 3x + 4x2 + -12 = 41 Reorder the terms: -12 + 3x + 4x2 = 41 Solving -12 + 3x + 4x2 = 41 Solving for variable 'x'. Reorder the terms: -12 + -41 + 3x + 4x2 = 41 + -41 Combine like terms: -12 + -41 = -53 -53 + 3x + 4x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -53 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '13.25' to each side of the equation. -13.25 + 0.75x + 13.25 + x2 = 0 + 13.25 Reorder the terms: -13.25 + 13.25 + 0.75x + x2 = 0 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + 0.75x + x2 = 0 + 13.25 0.75x + x2 = 0 + 13.25 Combine like terms: 0 + 13.25 = 13.25 0.75x + x2 = 13.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 13.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 13.25 + 0.140625 Combine like terms: 13.25 + 0.140625 = 13.390625 0.140625 + 0.75x + x2 = 13.390625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 13.390625 Calculate the square root of the right side: 3.659320292 Break this problem into two subproblems by setting (x + 0.375) equal to 3.659320292 and -3.659320292.Subproblem 1
x + 0.375 = 3.659320292 Simplifying x + 0.375 = 3.659320292 Reorder the terms: 0.375 + x = 3.659320292 Solving 0.375 + x = 3.659320292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 3.659320292 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 3.659320292 + -0.375 x = 3.659320292 + -0.375 Combine like terms: 3.659320292 + -0.375 = 3.284320292 x = 3.284320292 Simplifying x = 3.284320292Subproblem 2
x + 0.375 = -3.659320292 Simplifying x + 0.375 = -3.659320292 Reorder the terms: 0.375 + x = -3.659320292 Solving 0.375 + x = -3.659320292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -3.659320292 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -3.659320292 + -0.375 x = -3.659320292 + -0.375 Combine like terms: -3.659320292 + -0.375 = -4.034320292 x = -4.034320292 Simplifying x = -4.034320292Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.284320292, -4.034320292}
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