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Simplifying 3x2 + 2x + -147 = 0 Reorder the terms: -147 + 2x + 3x2 = 0 Solving -147 + 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'. -49 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 0.6666666667x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 0.6666666667x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 0.6666666667x + x2 = 0 + 49 0.6666666667x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 0.6666666667x + x2 = 49 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 = 49 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 49 + 0.1111111112 Combine like terms: 49 + 0.1111111112 = 49.1111111112 0.1111111112 + 0.6666666667x + x2 = 49.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 49.1111111112 Calculate the square root of the right side: 7.007932014 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 7.007932014 and -7.007932014.Subproblem 1
x + 0.3333333334 = 7.007932014 Simplifying x + 0.3333333334 = 7.007932014 Reorder the terms: 0.3333333334 + x = 7.007932014 Solving 0.3333333334 + x = 7.007932014 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 = 7.007932014 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 7.007932014 + -0.3333333334 x = 7.007932014 + -0.3333333334 Combine like terms: 7.007932014 + -0.3333333334 = 6.6745986806 x = 6.6745986806 Simplifying x = 6.6745986806Subproblem 2
x + 0.3333333334 = -7.007932014 Simplifying x + 0.3333333334 = -7.007932014 Reorder the terms: 0.3333333334 + x = -7.007932014 Solving 0.3333333334 + x = -7.007932014 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 = -7.007932014 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -7.007932014 + -0.3333333334 x = -7.007932014 + -0.3333333334 Combine like terms: -7.007932014 + -0.3333333334 = -7.3412653474 x = -7.3412653474 Simplifying x = -7.3412653474Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6745986806, -7.3412653474}
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