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Simplifying 0 = 3x2 + 18x + 7 Reorder the terms: 0 = 7 + 18x + 3x2 Solving 0 = 7 + 18x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -18x + -3x2 = 7 + 18x + 3x2 + -7 + -18x + -3x2 Reorder the terms: -7 + -18x + -3x2 = 7 + -7 + 18x + -18x + 3x2 + -3x2 Combine like terms: 7 + -7 = 0 -7 + -18x + -3x2 = 0 + 18x + -18x + 3x2 + -3x2 -7 + -18x + -3x2 = 18x + -18x + 3x2 + -3x2 Combine like terms: 18x + -18x = 0 -7 + -18x + -3x2 = 0 + 3x2 + -3x2 -7 + -18x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -7 + -18x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 18x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 18x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + 18x + 3x2 = 0 Solving 7 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 6x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 6x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 6x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 6x + x2 = 0 + -2.333333333 6x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 6x + x2 = -2.333333333 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 = -2.333333333 + 9 Reorder the terms: 9 + 6x + x2 = -2.333333333 + 9 Combine like terms: -2.333333333 + 9 = 6.666666667 9 + 6x + x2 = 6.666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 6.666666667 Calculate the square root of the right side: 2.581988898 Break this problem into two subproblems by setting (x + 3) equal to 2.581988898 and -2.581988898.Subproblem 1
x + 3 = 2.581988898 Simplifying x + 3 = 2.581988898 Reorder the terms: 3 + x = 2.581988898 Solving 3 + x = 2.581988898 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 = 2.581988898 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.581988898 + -3 x = 2.581988898 + -3 Combine like terms: 2.581988898 + -3 = -0.418011102 x = -0.418011102 Simplifying x = -0.418011102Subproblem 2
x + 3 = -2.581988898 Simplifying x + 3 = -2.581988898 Reorder the terms: 3 + x = -2.581988898 Solving 3 + x = -2.581988898 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 = -2.581988898 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.581988898 + -3 x = -2.581988898 + -3 Combine like terms: -2.581988898 + -3 = -5.581988898 x = -5.581988898 Simplifying x = -5.581988898Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.418011102, -5.581988898}Solution
x = {-0.418011102, -5.581988898}
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