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Simplifying 3x2 + 20x + -9 = 0 Reorder the terms: -9 + 20x + 3x2 = 0 Solving -9 + 20x + 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'. -3 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6.666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 6.666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6.666666667x + x2 = 0 + 3 6.666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 6.666666667x + x2 = 3 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 = 3 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 3 + 11.11111112 Combine like terms: 3 + 11.11111112 = 14.11111112 11.11111112 + 6.666666667x + x2 = 14.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 14.11111112 Calculate the square root of the right side: 3.756475891 Break this problem into two subproblems by setting (x + 3.333333334) equal to 3.756475891 and -3.756475891.Subproblem 1
x + 3.333333334 = 3.756475891 Simplifying x + 3.333333334 = 3.756475891 Reorder the terms: 3.333333334 + x = 3.756475891 Solving 3.333333334 + x = 3.756475891 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 = 3.756475891 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 3.756475891 + -3.333333334 x = 3.756475891 + -3.333333334 Combine like terms: 3.756475891 + -3.333333334 = 0.423142557 x = 0.423142557 Simplifying x = 0.423142557Subproblem 2
x + 3.333333334 = -3.756475891 Simplifying x + 3.333333334 = -3.756475891 Reorder the terms: 3.333333334 + x = -3.756475891 Solving 3.333333334 + x = -3.756475891 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 = -3.756475891 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -3.756475891 + -3.333333334 x = -3.756475891 + -3.333333334 Combine like terms: -3.756475891 + -3.333333334 = -7.089809225 x = -7.089809225 Simplifying x = -7.089809225Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.423142557, -7.089809225}
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