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Simplifying 3x2 + -2x + -6 = 24 Reorder the terms: -6 + -2x + 3x2 = 24 Solving -6 + -2x + 3x2 = 24 Solving for variable 'x'. Reorder the terms: -6 + -24 + -2x + 3x2 = 24 + -24 Combine like terms: -6 + -24 = -30 -30 + -2x + 3x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -30 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.6666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -0.6666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.6666666667x + x2 = 0 + 10 -0.6666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.6666666667x + x2 = 10 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 = 10 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 10 + 0.1111111112 Combine like terms: 10 + 0.1111111112 = 10.1111111112 0.1111111112 + -0.6666666667x + x2 = 10.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 10.1111111112 Calculate the square root of the right side: 3.179797338 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 3.179797338 and -3.179797338.Subproblem 1
x + -0.3333333334 = 3.179797338 Simplifying x + -0.3333333334 = 3.179797338 Reorder the terms: -0.3333333334 + x = 3.179797338 Solving -0.3333333334 + x = 3.179797338 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 = 3.179797338 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 3.179797338 + 0.3333333334 x = 3.179797338 + 0.3333333334 Combine like terms: 3.179797338 + 0.3333333334 = 3.5131306714 x = 3.5131306714 Simplifying x = 3.5131306714Subproblem 2
x + -0.3333333334 = -3.179797338 Simplifying x + -0.3333333334 = -3.179797338 Reorder the terms: -0.3333333334 + x = -3.179797338 Solving -0.3333333334 + x = -3.179797338 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 = -3.179797338 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -3.179797338 + 0.3333333334 x = -3.179797338 + 0.3333333334 Combine like terms: -3.179797338 + 0.3333333334 = -2.8464640046 x = -2.8464640046 Simplifying x = -2.8464640046Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5131306714, -2.8464640046}
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