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Simplifying 0 = 3x2 + 9x + 4 Reorder the terms: 0 = 4 + 9x + 3x2 Solving 0 = 4 + 9x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -9x + -3x2 = 4 + 9x + 3x2 + -4 + -9x + -3x2 Reorder the terms: -4 + -9x + -3x2 = 4 + -4 + 9x + -9x + 3x2 + -3x2 Combine like terms: 4 + -4 = 0 -4 + -9x + -3x2 = 0 + 9x + -9x + 3x2 + -3x2 -4 + -9x + -3x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 -4 + -9x + -3x2 = 0 + 3x2 + -3x2 -4 + -9x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -4 + -9x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 9x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 9x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 9x + 3x2 = 0 Solving 4 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 3x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 3x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 3x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 3x + x2 = 0 + -1.333333333 3x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 3x + x2 = -1.333333333 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1.333333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.333333333 + 2.25 Combine like terms: -1.333333333 + 2.25 = 0.916666667 2.25 + 3x + x2 = 0.916666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 0.916666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (x + 1.5) equal to 0.957427108 and -0.957427108.Subproblem 1
x + 1.5 = 0.957427108 Simplifying x + 1.5 = 0.957427108 Reorder the terms: 1.5 + x = 0.957427108 Solving 1.5 + x = 0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.957427108 + -1.5 x = 0.957427108 + -1.5 Combine like terms: 0.957427108 + -1.5 = -0.542572892 x = -0.542572892 Simplifying x = -0.542572892Subproblem 2
x + 1.5 = -0.957427108 Simplifying x + 1.5 = -0.957427108 Reorder the terms: 1.5 + x = -0.957427108 Solving 1.5 + x = -0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.957427108 + -1.5 x = -0.957427108 + -1.5 Combine like terms: -0.957427108 + -1.5 = -2.457427108 x = -2.457427108 Simplifying x = -2.457427108Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.542572892, -2.457427108}Solution
x = {-0.542572892, -2.457427108}
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