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Simplifying 3x2 + 2x + -144 = 0 Reorder the terms: -144 + 2x + 3x2 = 0 Solving -144 + 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'. -48 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 0.6666666667x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 0.6666666667x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 0.6666666667x + x2 = 0 + 48 0.6666666667x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 0.6666666667x + x2 = 48 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 = 48 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 48 + 0.1111111112 Combine like terms: 48 + 0.1111111112 = 48.1111111112 0.1111111112 + 0.6666666667x + x2 = 48.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 48.1111111112 Calculate the square root of the right side: 6.936217349 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 6.936217349 and -6.936217349.Subproblem 1
x + 0.3333333334 = 6.936217349 Simplifying x + 0.3333333334 = 6.936217349 Reorder the terms: 0.3333333334 + x = 6.936217349 Solving 0.3333333334 + x = 6.936217349 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 = 6.936217349 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 6.936217349 + -0.3333333334 x = 6.936217349 + -0.3333333334 Combine like terms: 6.936217349 + -0.3333333334 = 6.6028840156 x = 6.6028840156 Simplifying x = 6.6028840156Subproblem 2
x + 0.3333333334 = -6.936217349 Simplifying x + 0.3333333334 = -6.936217349 Reorder the terms: 0.3333333334 + x = -6.936217349 Solving 0.3333333334 + x = -6.936217349 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 = -6.936217349 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -6.936217349 + -0.3333333334 x = -6.936217349 + -0.3333333334 Combine like terms: -6.936217349 + -0.3333333334 = -7.2695506824 x = -7.2695506824 Simplifying x = -7.2695506824Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6028840156, -7.2695506824}
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