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Simplifying 3x2 + 18x + 13 = 0 Reorder the terms: 13 + 18x + 3x2 = 0 Solving 13 + 18x + 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'. 4.333333333 + 6x + x2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + 6x + -4.333333333 + x2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + 6x + x2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + 6x + x2 = 0 + -4.333333333 6x + x2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 6x + x2 = -4.333333333 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -4.333333333 + 9 Reorder the terms: 9 + 6x + x2 = -4.333333333 + 9 Combine like terms: -4.333333333 + 9 = 4.666666667 9 + 6x + x2 = 4.666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 4.666666667 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (x + 3) equal to 2.1602469 and -2.1602469.Subproblem 1
x + 3 = 2.1602469 Simplifying x + 3 = 2.1602469 Reorder the terms: 3 + x = 2.1602469 Solving 3 + x = 2.1602469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.1602469 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.1602469 + -3 x = 2.1602469 + -3 Combine like terms: 2.1602469 + -3 = -0.8397531 x = -0.8397531 Simplifying x = -0.8397531Subproblem 2
x + 3 = -2.1602469 Simplifying x + 3 = -2.1602469 Reorder the terms: 3 + x = -2.1602469 Solving 3 + x = -2.1602469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.1602469 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.1602469 + -3 x = -2.1602469 + -3 Combine like terms: -2.1602469 + -3 = -5.1602469 x = -5.1602469 Simplifying x = -5.1602469Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.8397531, -5.1602469}
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