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Simplifying 3x(4x + -3) = 11 Reorder the terms: 3x(-3 + 4x) = 11 (-3 * 3x + 4x * 3x) = 11 (-9x + 12x2) = 11 Solving -9x + 12x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -9x + 12x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -9x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.9166666667 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -0.75x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -0.75x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -0.75x + x2 = 0 + 0.9166666667 -0.75x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -0.75x + x2 = 0.9166666667 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 = 0.9166666667 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.9166666667 + 0.140625 Combine like terms: 0.9166666667 + 0.140625 = 1.0572916667 0.140625 + -0.75x + x2 = 1.0572916667 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 1.0572916667 Calculate the square root of the right side: 1.02824689 Break this problem into two subproblems by setting (x + -0.375) equal to 1.02824689 and -1.02824689.Subproblem 1
x + -0.375 = 1.02824689 Simplifying x + -0.375 = 1.02824689 Reorder the terms: -0.375 + x = 1.02824689 Solving -0.375 + x = 1.02824689 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 = 1.02824689 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.02824689 + 0.375 x = 1.02824689 + 0.375 Combine like terms: 1.02824689 + 0.375 = 1.40324689 x = 1.40324689 Simplifying x = 1.40324689Subproblem 2
x + -0.375 = -1.02824689 Simplifying x + -0.375 = -1.02824689 Reorder the terms: -0.375 + x = -1.02824689 Solving -0.375 + x = -1.02824689 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 = -1.02824689 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.02824689 + 0.375 x = -1.02824689 + 0.375 Combine like terms: -1.02824689 + 0.375 = -0.65324689 x = -0.65324689 Simplifying x = -0.65324689Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.40324689, -0.65324689}
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