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Simplifying 9x2 + 60x + 13 = 0 Reorder the terms: 13 + 60x + 9x2 = 0 Solving 13 + 60x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.444444444 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '-1.444444444' to each side of the equation. 1.444444444 + 6.666666667x + -1.444444444 + x2 = 0 + -1.444444444 Reorder the terms: 1.444444444 + -1.444444444 + 6.666666667x + x2 = 0 + -1.444444444 Combine like terms: 1.444444444 + -1.444444444 = 0.000000000 0.000000000 + 6.666666667x + x2 = 0 + -1.444444444 6.666666667x + x2 = 0 + -1.444444444 Combine like terms: 0 + -1.444444444 = -1.444444444 6.666666667x + x2 = -1.444444444 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 = -1.444444444 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = -1.444444444 + 11.11111112 Combine like terms: -1.444444444 + 11.11111112 = 9.666666676 11.11111112 + 6.666666667x + x2 = 9.666666676 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 9.666666676 Calculate the square root of the right side: 3.109126353 Break this problem into two subproblems by setting (x + 3.333333334) equal to 3.109126353 and -3.109126353.Subproblem 1
x + 3.333333334 = 3.109126353 Simplifying x + 3.333333334 = 3.109126353 Reorder the terms: 3.333333334 + x = 3.109126353 Solving 3.333333334 + x = 3.109126353 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 = 3.109126353 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 3.109126353 + -3.333333334 x = 3.109126353 + -3.333333334 Combine like terms: 3.109126353 + -3.333333334 = -0.224206981 x = -0.224206981 Simplifying x = -0.224206981Subproblem 2
x + 3.333333334 = -3.109126353 Simplifying x + 3.333333334 = -3.109126353 Reorder the terms: 3.333333334 + x = -3.109126353 Solving 3.333333334 + x = -3.109126353 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 = -3.109126353 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -3.109126353 + -3.333333334 x = -3.109126353 + -3.333333334 Combine like terms: -3.109126353 + -3.333333334 = -6.442459687 x = -6.442459687 Simplifying x = -6.442459687Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.224206981, -6.442459687}
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