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Simplifying 0 = 59 + -0.3x2 + -2x + 12 Reorder the terms: 0 = 59 + 12 + -2x + -0.3x2 Combine like terms: 59 + 12 = 71 0 = 71 + -2x + -0.3x2 Solving 0 = 71 + -2x + -0.3x2 Solving for variable 'x'. Combine like terms: 0 + -71 = -71 -71 + 2x + 0.3x2 = 71 + -2x + -0.3x2 + -71 + 2x + 0.3x2 Reorder the terms: -71 + 2x + 0.3x2 = 71 + -71 + -2x + 2x + -0.3x2 + 0.3x2 Combine like terms: 71 + -71 = 0 -71 + 2x + 0.3x2 = 0 + -2x + 2x + -0.3x2 + 0.3x2 -71 + 2x + 0.3x2 = -2x + 2x + -0.3x2 + 0.3x2 Combine like terms: -2x + 2x = 0 -71 + 2x + 0.3x2 = 0 + -0.3x2 + 0.3x2 -71 + 2x + 0.3x2 = -0.3x2 + 0.3x2 Combine like terms: -0.3x2 + 0.3x2 = 0.0 -71 + 2x + 0.3x2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -236.6666667 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '236.6666667' to each side of the equation. -236.6666667 + 6.666666667x + 236.6666667 + x2 = 0 + 236.6666667 Reorder the terms: -236.6666667 + 236.6666667 + 6.666666667x + x2 = 0 + 236.6666667 Combine like terms: -236.6666667 + 236.6666667 = 0.0000000 0.0000000 + 6.666666667x + x2 = 0 + 236.6666667 6.666666667x + x2 = 0 + 236.6666667 Combine like terms: 0 + 236.6666667 = 236.6666667 6.666666667x + x2 = 236.6666667 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 236.6666667 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 236.6666667 + 11.11111112 Combine like terms: 236.6666667 + 11.11111112 = 247.77777782 11.11111112 + 6.666666667x + x2 = 247.77777782 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 247.77777782 Calculate the square root of the right side: 15.740958605 Break this problem into two subproblems by setting (x + 3.333333334) equal to 15.740958605 and -15.740958605.Subproblem 1
x + 3.333333334 = 15.740958605 Simplifying x + 3.333333334 = 15.740958605 Reorder the terms: 3.333333334 + x = 15.740958605 Solving 3.333333334 + x = 15.740958605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 15.740958605 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 15.740958605 + -3.333333334 x = 15.740958605 + -3.333333334 Combine like terms: 15.740958605 + -3.333333334 = 12.407625271 x = 12.407625271 Simplifying x = 12.407625271Subproblem 2
x + 3.333333334 = -15.740958605 Simplifying x + 3.333333334 = -15.740958605 Reorder the terms: 3.333333334 + x = -15.740958605 Solving 3.333333334 + x = -15.740958605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -15.740958605 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -15.740958605 + -3.333333334 x = -15.740958605 + -3.333333334 Combine like terms: -15.740958605 + -3.333333334 = -19.074291939 x = -19.074291939 Simplifying x = -19.074291939Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.407625271, -19.074291939}
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