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Simplifying 12x * 3 + -4x2 + 3x + -1 = 0 Reorder the terms for easier multiplication: 12 * 3x + -4x2 + 3x + -1 = 0 Multiply 12 * 3 36x + -4x2 + 3x + -1 = 0 Reorder the terms: -1 + 36x + 3x + -4x2 = 0 Combine like terms: 36x + 3x = 39x -1 + 39x + -4x2 = 0 Solving -1 + 39x + -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'. 0.25 + -9.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -9.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -9.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -9.75x + x2 = 0 + -0.25 -9.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -9.75x + x2 = -0.25 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = -0.25 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = -0.25 + 23.765625 Combine like terms: -0.25 + 23.765625 = 23.515625 23.765625 + -9.75x + x2 = 23.515625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 23.515625 Calculate the square root of the right side: 4.849291185 Break this problem into two subproblems by setting (x + -4.875) equal to 4.849291185 and -4.849291185.Subproblem 1
x + -4.875 = 4.849291185 Simplifying x + -4.875 = 4.849291185 Reorder the terms: -4.875 + x = 4.849291185 Solving -4.875 + x = 4.849291185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 4.849291185 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 4.849291185 + 4.875 x = 4.849291185 + 4.875 Combine like terms: 4.849291185 + 4.875 = 9.724291185 x = 9.724291185 Simplifying x = 9.724291185Subproblem 2
x + -4.875 = -4.849291185 Simplifying x + -4.875 = -4.849291185 Reorder the terms: -4.875 + x = -4.849291185 Solving -4.875 + x = -4.849291185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -4.849291185 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -4.849291185 + 4.875 x = -4.849291185 + 4.875 Combine like terms: -4.849291185 + 4.875 = 0.025708815 x = 0.025708815 Simplifying x = 0.025708815Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.724291185, 0.025708815}
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