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Simplifying 3x2 + -32x + 12 = 0 Reorder the terms: 12 + -32x + 3x2 = 0 Solving 12 + -32x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10.66666667x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -10.66666667x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10.66666667x + x2 = 0 + -4 -10.66666667x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10.66666667x + x2 = -4 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 = -4 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = -4 + 28.44444446 Combine like terms: -4 + 28.44444446 = 24.44444446 28.44444446 + -10.66666667x + x2 = 24.44444446 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 24.44444446 Calculate the square root of the right side: 4.944132326 Break this problem into two subproblems by setting (x + -5.333333335) equal to 4.944132326 and -4.944132326.Subproblem 1
x + -5.333333335 = 4.944132326 Simplifying x + -5.333333335 = 4.944132326 Reorder the terms: -5.333333335 + x = 4.944132326 Solving -5.333333335 + x = 4.944132326 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 = 4.944132326 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 4.944132326 + 5.333333335 x = 4.944132326 + 5.333333335 Combine like terms: 4.944132326 + 5.333333335 = 10.277465661 x = 10.277465661 Simplifying x = 10.277465661Subproblem 2
x + -5.333333335 = -4.944132326 Simplifying x + -5.333333335 = -4.944132326 Reorder the terms: -5.333333335 + x = -4.944132326 Solving -5.333333335 + x = -4.944132326 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 = -4.944132326 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -4.944132326 + 5.333333335 x = -4.944132326 + 5.333333335 Combine like terms: -4.944132326 + 5.333333335 = 0.389201009 x = 0.389201009 Simplifying x = 0.389201009Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.277465661, 0.389201009}
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