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Simplifying 3x2 = -2x + 24 Reorder the terms: 3x2 = 24 + -2x Solving 3x2 = 24 + -2x Solving for variable 'x'. Reorder the terms: -24 + 2x + 3x2 = 24 + -2x + -24 + 2x Reorder the terms: -24 + 2x + 3x2 = 24 + -24 + -2x + 2x Combine like terms: 24 + -24 = 0 -24 + 2x + 3x2 = 0 + -2x + 2x -24 + 2x + 3x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -24 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 0.6666666667x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 0.6666666667x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 0.6666666667x + x2 = 0 + 8 0.6666666667x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 0.6666666667x + x2 = 8 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 8 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 8 + 0.1111111112 Combine like terms: 8 + 0.1111111112 = 8.1111111112 0.1111111112 + 0.6666666667x + x2 = 8.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 8.1111111112 Calculate the square root of the right side: 2.848001248 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 2.848001248 and -2.848001248.Subproblem 1
x + 0.3333333334 = 2.848001248 Simplifying x + 0.3333333334 = 2.848001248 Reorder the terms: 0.3333333334 + x = 2.848001248 Solving 0.3333333334 + x = 2.848001248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 2.848001248 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 2.848001248 + -0.3333333334 x = 2.848001248 + -0.3333333334 Combine like terms: 2.848001248 + -0.3333333334 = 2.5146679146 x = 2.5146679146 Simplifying x = 2.5146679146Subproblem 2
x + 0.3333333334 = -2.848001248 Simplifying x + 0.3333333334 = -2.848001248 Reorder the terms: 0.3333333334 + x = -2.848001248 Solving 0.3333333334 + x = -2.848001248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -2.848001248 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -2.848001248 + -0.3333333334 x = -2.848001248 + -0.3333333334 Combine like terms: -2.848001248 + -0.3333333334 = -3.1813345814 x = -3.1813345814 Simplifying x = -3.1813345814Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5146679146, -3.1813345814}
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