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Simplifying 0.33x2 + 3x + -4 = 4 Reorder the terms: -4 + 3x + 0.33x2 = 4 Solving -4 + 3x + 0.33x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -4 + 3x + 0.33x2 = 4 + -4 Combine like terms: -4 + -4 = -8 -8 + 3x + 0.33x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -8 + 3x + 0.33x2 = 0 Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. -24.24242424 + 9.090909091x + x2 = 0 Move the constant term to the right: Add '24.24242424' to each side of the equation. -24.24242424 + 9.090909091x + 24.24242424 + x2 = 0 + 24.24242424 Reorder the terms: -24.24242424 + 24.24242424 + 9.090909091x + x2 = 0 + 24.24242424 Combine like terms: -24.24242424 + 24.24242424 = 0.00000000 0.00000000 + 9.090909091x + x2 = 0 + 24.24242424 9.090909091x + x2 = 0 + 24.24242424 Combine like terms: 0 + 24.24242424 = 24.24242424 9.090909091x + x2 = 24.24242424 The x term is 9.090909091x. Take half its coefficient (4.545454546). Square it (20.66115703) and add it to both sides. Add '20.66115703' to each side of the equation. 9.090909091x + 20.66115703 + x2 = 24.24242424 + 20.66115703 Reorder the terms: 20.66115703 + 9.090909091x + x2 = 24.24242424 + 20.66115703 Combine like terms: 24.24242424 + 20.66115703 = 44.90358127 20.66115703 + 9.090909091x + x2 = 44.90358127 Factor a perfect square on the left side: (x + 4.545454546)(x + 4.545454546) = 44.90358127 Calculate the square root of the right side: 6.701013451 Break this problem into two subproblems by setting (x + 4.545454546) equal to 6.701013451 and -6.701013451.Subproblem 1
x + 4.545454546 = 6.701013451 Simplifying x + 4.545454546 = 6.701013451 Reorder the terms: 4.545454546 + x = 6.701013451 Solving 4.545454546 + x = 6.701013451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.545454546' to each side of the equation. 4.545454546 + -4.545454546 + x = 6.701013451 + -4.545454546 Combine like terms: 4.545454546 + -4.545454546 = 0.000000000 0.000000000 + x = 6.701013451 + -4.545454546 x = 6.701013451 + -4.545454546 Combine like terms: 6.701013451 + -4.545454546 = 2.155558905 x = 2.155558905 Simplifying x = 2.155558905Subproblem 2
x + 4.545454546 = -6.701013451 Simplifying x + 4.545454546 = -6.701013451 Reorder the terms: 4.545454546 + x = -6.701013451 Solving 4.545454546 + x = -6.701013451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.545454546' to each side of the equation. 4.545454546 + -4.545454546 + x = -6.701013451 + -4.545454546 Combine like terms: 4.545454546 + -4.545454546 = 0.000000000 0.000000000 + x = -6.701013451 + -4.545454546 x = -6.701013451 + -4.545454546 Combine like terms: -6.701013451 + -4.545454546 = -11.246467997 x = -11.246467997 Simplifying x = -11.246467997Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.155558905, -11.246467997}
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