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Simplifying 3x2 + -2x + -48 = 0 Reorder the terms: -48 + -2x + 3x2 = 0 Solving -48 + -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'. -16 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -0.6666666667x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -0.6666666667x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -0.6666666667x + x2 = 0 + 16 -0.6666666667x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -0.6666666667x + x2 = 16 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 = 16 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 16 + 0.1111111112 Combine like terms: 16 + 0.1111111112 = 16.1111111112 0.1111111112 + -0.6666666667x + x2 = 16.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 16.1111111112 Calculate the square root of the right side: 4.01386486 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 4.01386486 and -4.01386486.Subproblem 1
x + -0.3333333334 = 4.01386486 Simplifying x + -0.3333333334 = 4.01386486 Reorder the terms: -0.3333333334 + x = 4.01386486 Solving -0.3333333334 + x = 4.01386486 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 = 4.01386486 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 4.01386486 + 0.3333333334 x = 4.01386486 + 0.3333333334 Combine like terms: 4.01386486 + 0.3333333334 = 4.3471981934 x = 4.3471981934 Simplifying x = 4.3471981934Subproblem 2
x + -0.3333333334 = -4.01386486 Simplifying x + -0.3333333334 = -4.01386486 Reorder the terms: -0.3333333334 + x = -4.01386486 Solving -0.3333333334 + x = -4.01386486 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 = -4.01386486 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -4.01386486 + 0.3333333334 x = -4.01386486 + 0.3333333334 Combine like terms: -4.01386486 + 0.3333333334 = -3.6805315266 x = -3.6805315266 Simplifying x = -3.6805315266Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.3471981934, -3.6805315266}
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