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Simplifying 0 = -3x2 + 32x + 33 Reorder the terms: 0 = 33 + 32x + -3x2 Solving 0 = 33 + 32x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -33 = -33 -33 + -32x + 3x2 = 33 + 32x + -3x2 + -33 + -32x + 3x2 Reorder the terms: -33 + -32x + 3x2 = 33 + -33 + 32x + -32x + -3x2 + 3x2 Combine like terms: 33 + -33 = 0 -33 + -32x + 3x2 = 0 + 32x + -32x + -3x2 + 3x2 -33 + -32x + 3x2 = 32x + -32x + -3x2 + 3x2 Combine like terms: 32x + -32x = 0 -33 + -32x + 3x2 = 0 + -3x2 + 3x2 -33 + -32x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -33 + -32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -10.66666667x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -10.66666667x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -10.66666667x + x2 = 0 + 11 -10.66666667x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -10.66666667x + x2 = 11 The x term is -10.66666667x. Take half its coefficient (-5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. -10.66666667x + 28.44444446 + x2 = 11 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = 11 + 28.44444446 Combine like terms: 11 + 28.44444446 = 39.44444446 28.44444446 + -10.66666667x + x2 = 39.44444446 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 39.44444446 Calculate the square root of the right side: 6.280481228 Break this problem into two subproblems by setting (x + -5.333333335) equal to 6.280481228 and -6.280481228.Subproblem 1
x + -5.333333335 = 6.280481228 Simplifying x + -5.333333335 = 6.280481228 Reorder the terms: -5.333333335 + x = 6.280481228 Solving -5.333333335 + x = 6.280481228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = 6.280481228 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 6.280481228 + 5.333333335 x = 6.280481228 + 5.333333335 Combine like terms: 6.280481228 + 5.333333335 = 11.613814563 x = 11.613814563 Simplifying x = 11.613814563Subproblem 2
x + -5.333333335 = -6.280481228 Simplifying x + -5.333333335 = -6.280481228 Reorder the terms: -5.333333335 + x = -6.280481228 Solving -5.333333335 + x = -6.280481228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = -6.280481228 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -6.280481228 + 5.333333335 x = -6.280481228 + 5.333333335 Combine like terms: -6.280481228 + 5.333333335 = -0.947147893 x = -0.947147893 Simplifying x = -0.947147893Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.613814563, -0.947147893}
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