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Simplifying 0.33x2 + -2x + 3 = 0 Reorder the terms: 3 + -2x + 0.33x2 = 0 Solving 3 + -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'. 9.090909091 + -6.060606061x + x2 = 0 Move the constant term to the right: Add '-9.090909091' to each side of the equation. 9.090909091 + -6.060606061x + -9.090909091 + x2 = 0 + -9.090909091 Reorder the terms: 9.090909091 + -9.090909091 + -6.060606061x + x2 = 0 + -9.090909091 Combine like terms: 9.090909091 + -9.090909091 = 0.000000000 0.000000000 + -6.060606061x + x2 = 0 + -9.090909091 -6.060606061x + x2 = 0 + -9.090909091 Combine like terms: 0 + -9.090909091 = -9.090909091 -6.060606061x + x2 = -9.090909091 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 = -9.090909091 + 9.182736460 Reorder the terms: 9.182736460 + -6.060606061x + x2 = -9.090909091 + 9.182736460 Combine like terms: -9.090909091 + 9.182736460 = 0.091827369 9.182736460 + -6.060606061x + x2 = 0.091827369 Factor a perfect square on the left side: (x + -3.030303031)(x + -3.030303031) = 0.091827369 Calculate the square root of the right side: 0.30303031 Break this problem into two subproblems by setting (x + -3.030303031) equal to 0.30303031 and -0.30303031.Subproblem 1
x + -3.030303031 = 0.30303031 Simplifying x + -3.030303031 = 0.30303031 Reorder the terms: -3.030303031 + x = 0.30303031 Solving -3.030303031 + x = 0.30303031 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 = 0.30303031 + 3.030303031 Combine like terms: -3.030303031 + 3.030303031 = 0.000000000 0.000000000 + x = 0.30303031 + 3.030303031 x = 0.30303031 + 3.030303031 Combine like terms: 0.30303031 + 3.030303031 = 3.333333341 x = 3.333333341 Simplifying x = 3.333333341Subproblem 2
x + -3.030303031 = -0.30303031 Simplifying x + -3.030303031 = -0.30303031 Reorder the terms: -3.030303031 + x = -0.30303031 Solving -3.030303031 + x = -0.30303031 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 = -0.30303031 + 3.030303031 Combine like terms: -3.030303031 + 3.030303031 = 0.000000000 0.000000000 + x = -0.30303031 + 3.030303031 x = -0.30303031 + 3.030303031 Combine like terms: -0.30303031 + 3.030303031 = 2.727272721 x = 2.727272721 Simplifying x = 2.727272721Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.333333341, 2.727272721}
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