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Simplifying 3x2 + 18x + -14 = 0 Reorder the terms: -14 + 18x + 3x2 = 0 Solving -14 + 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'. -4.666666667 + 6x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + 6x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + 6x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + 6x + x2 = 0 + 4.666666667 6x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 6x + x2 = 4.666666667 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 = 4.666666667 + 9 Reorder the terms: 9 + 6x + x2 = 4.666666667 + 9 Combine like terms: 4.666666667 + 9 = 13.666666667 9 + 6x + x2 = 13.666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 13.666666667 Calculate the square root of the right side: 3.696845502 Break this problem into two subproblems by setting (x + 3) equal to 3.696845502 and -3.696845502.Subproblem 1
x + 3 = 3.696845502 Simplifying x + 3 = 3.696845502 Reorder the terms: 3 + x = 3.696845502 Solving 3 + x = 3.696845502 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 = 3.696845502 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.696845502 + -3 x = 3.696845502 + -3 Combine like terms: 3.696845502 + -3 = 0.696845502 x = 0.696845502 Simplifying x = 0.696845502Subproblem 2
x + 3 = -3.696845502 Simplifying x + 3 = -3.696845502 Reorder the terms: 3 + x = -3.696845502 Solving 3 + x = -3.696845502 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 = -3.696845502 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.696845502 + -3 x = -3.696845502 + -3 Combine like terms: -3.696845502 + -3 = -6.696845502 x = -6.696845502 Simplifying x = -6.696845502Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.696845502, -6.696845502}
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