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Simplifying 3x2 + -12x + 9 = 3.84 Reorder the terms: 9 + -12x + 3x2 = 3.84 Solving 9 + -12x + 3x2 = 3.84 Solving for variable 'x'. Reorder the terms: 9 + -3.84 + -12x + 3x2 = 3.84 + -3.84 Combine like terms: 9 + -3.84 = 5.16 5.16 + -12x + 3x2 = 3.84 + -3.84 Combine like terms: 3.84 + -3.84 = 0.00 5.16 + -12x + 3x2 = 0.00 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.72 + -4x + x2 = 0.00 Move the constant term to the right: Add '-1.72' to each side of the equation. 1.72 + -4x + -1.72 + x2 = 0.00 + -1.72 Reorder the terms: 1.72 + -1.72 + -4x + x2 = 0.00 + -1.72 Combine like terms: 1.72 + -1.72 = 0.00 0.00 + -4x + x2 = 0.00 + -1.72 -4x + x2 = 0.00 + -1.72 Combine like terms: 0.00 + -1.72 = -1.72 -4x + x2 = -1.72 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1.72 + 4 Reorder the terms: 4 + -4x + x2 = -1.72 + 4 Combine like terms: -1.72 + 4 = 2.28 4 + -4x + x2 = 2.28 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.28 Calculate the square root of the right side: 1.509966887 Break this problem into two subproblems by setting (x + -2) equal to 1.509966887 and -1.509966887.Subproblem 1
x + -2 = 1.509966887 Simplifying x + -2 = 1.509966887 Reorder the terms: -2 + x = 1.509966887 Solving -2 + x = 1.509966887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.509966887 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.509966887 + 2 x = 1.509966887 + 2 Combine like terms: 1.509966887 + 2 = 3.509966887 x = 3.509966887 Simplifying x = 3.509966887Subproblem 2
x + -2 = -1.509966887 Simplifying x + -2 = -1.509966887 Reorder the terms: -2 + x = -1.509966887 Solving -2 + x = -1.509966887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.509966887 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.509966887 + 2 x = -1.509966887 + 2 Combine like terms: -1.509966887 + 2 = 0.490033113 x = 0.490033113 Simplifying x = 0.490033113Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.509966887, 0.490033113}
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