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Simplifying 3x2 + 2x + -63 = 0 Reorder the terms: -63 + 2x + 3x2 = 0 Solving -63 + 2x + 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'. -21 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 0.6666666667x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 0.6666666667x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 0.6666666667x + x2 = 0 + 21 0.6666666667x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 0.6666666667x + x2 = 21 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 = 21 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 21 + 0.1111111112 Combine like terms: 21 + 0.1111111112 = 21.1111111112 0.1111111112 + 0.6666666667x + x2 = 21.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 21.1111111112 Calculate the square root of the right side: 4.594682917 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 4.594682917 and -4.594682917.Subproblem 1
x + 0.3333333334 = 4.594682917 Simplifying x + 0.3333333334 = 4.594682917 Reorder the terms: 0.3333333334 + x = 4.594682917 Solving 0.3333333334 + x = 4.594682917 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 = 4.594682917 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 4.594682917 + -0.3333333334 x = 4.594682917 + -0.3333333334 Combine like terms: 4.594682917 + -0.3333333334 = 4.2613495836 x = 4.2613495836 Simplifying x = 4.2613495836Subproblem 2
x + 0.3333333334 = -4.594682917 Simplifying x + 0.3333333334 = -4.594682917 Reorder the terms: 0.3333333334 + x = -4.594682917 Solving 0.3333333334 + x = -4.594682917 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 = -4.594682917 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -4.594682917 + -0.3333333334 x = -4.594682917 + -0.3333333334 Combine like terms: -4.594682917 + -0.3333333334 = -4.9280162504 x = -4.9280162504 Simplifying x = -4.9280162504Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2613495836, -4.9280162504}
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