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Simplifying 3x2 + 18x + 23 = 0 Reorder the terms: 23 + 18x + 3x2 = 0 Solving 23 + 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'. 7.666666667 + 6x + x2 = 0 Move the constant term to the right: Add '-7.666666667' to each side of the equation. 7.666666667 + 6x + -7.666666667 + x2 = 0 + -7.666666667 Reorder the terms: 7.666666667 + -7.666666667 + 6x + x2 = 0 + -7.666666667 Combine like terms: 7.666666667 + -7.666666667 = 0.000000000 0.000000000 + 6x + x2 = 0 + -7.666666667 6x + x2 = 0 + -7.666666667 Combine like terms: 0 + -7.666666667 = -7.666666667 6x + x2 = -7.666666667 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 = -7.666666667 + 9 Reorder the terms: 9 + 6x + x2 = -7.666666667 + 9 Combine like terms: -7.666666667 + 9 = 1.333333333 9 + 6x + x2 = 1.333333333 Factor a perfect square on the left side: (x + 3)(x + 3) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (x + 3) equal to 1.154700538 and -1.154700538.Subproblem 1
x + 3 = 1.154700538 Simplifying x + 3 = 1.154700538 Reorder the terms: 3 + x = 1.154700538 Solving 3 + x = 1.154700538 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 = 1.154700538 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.154700538 + -3 x = 1.154700538 + -3 Combine like terms: 1.154700538 + -3 = -1.845299462 x = -1.845299462 Simplifying x = -1.845299462Subproblem 2
x + 3 = -1.154700538 Simplifying x + 3 = -1.154700538 Reorder the terms: 3 + x = -1.154700538 Solving 3 + x = -1.154700538 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 = -1.154700538 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.154700538 + -3 x = -1.154700538 + -3 Combine like terms: -1.154700538 + -3 = -4.154700538 x = -4.154700538 Simplifying x = -4.154700538Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.845299462, -4.154700538}
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