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Simplifying 0.33x2 + 2x + -4 = 0 Reorder the terms: -4 + 2x + 0.33x2 = 0 Solving -4 + 2x + 0.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. -12.12121212 + 6.060606061x + x2 = 0 Move the constant term to the right: Add '12.12121212' to each side of the equation. -12.12121212 + 6.060606061x + 12.12121212 + x2 = 0 + 12.12121212 Reorder the terms: -12.12121212 + 12.12121212 + 6.060606061x + x2 = 0 + 12.12121212 Combine like terms: -12.12121212 + 12.12121212 = 0.00000000 0.00000000 + 6.060606061x + x2 = 0 + 12.12121212 6.060606061x + x2 = 0 + 12.12121212 Combine like terms: 0 + 12.12121212 = 12.12121212 6.060606061x + x2 = 12.12121212 The x term is 6.060606061x. Take half its coefficient (3.030303031). Square it (9.182736460) and add it to both sides. Add '9.182736460' to each side of the equation. 6.060606061x + 9.182736460 + x2 = 12.12121212 + 9.182736460 Reorder the terms: 9.182736460 + 6.060606061x + x2 = 12.12121212 + 9.182736460 Combine like terms: 12.12121212 + 9.182736460 = 21.30394858 9.182736460 + 6.060606061x + x2 = 21.30394858 Factor a perfect square on the left side: (x + 3.030303031)(x + 3.030303031) = 21.30394858 Calculate the square root of the right side: 4.615620065 Break this problem into two subproblems by setting (x + 3.030303031) equal to 4.615620065 and -4.615620065.Subproblem 1
x + 3.030303031 = 4.615620065 Simplifying x + 3.030303031 = 4.615620065 Reorder the terms: 3.030303031 + x = 4.615620065 Solving 3.030303031 + x = 4.615620065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.030303031' to each side of the equation. 3.030303031 + -3.030303031 + x = 4.615620065 + -3.030303031 Combine like terms: 3.030303031 + -3.030303031 = 0.000000000 0.000000000 + x = 4.615620065 + -3.030303031 x = 4.615620065 + -3.030303031 Combine like terms: 4.615620065 + -3.030303031 = 1.585317034 x = 1.585317034 Simplifying x = 1.585317034Subproblem 2
x + 3.030303031 = -4.615620065 Simplifying x + 3.030303031 = -4.615620065 Reorder the terms: 3.030303031 + x = -4.615620065 Solving 3.030303031 + x = -4.615620065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.030303031' to each side of the equation. 3.030303031 + -3.030303031 + x = -4.615620065 + -3.030303031 Combine like terms: 3.030303031 + -3.030303031 = 0.000000000 0.000000000 + x = -4.615620065 + -3.030303031 x = -4.615620065 + -3.030303031 Combine like terms: -4.615620065 + -3.030303031 = -7.645923096 x = -7.645923096 Simplifying x = -7.645923096Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.585317034, -7.645923096}
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