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Simplifying 0 = 3x2 + 9x + 1 Reorder the terms: 0 = 1 + 9x + 3x2 Solving 0 = 1 + 9x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -9x + -3x2 = 1 + 9x + 3x2 + -1 + -9x + -3x2 Reorder the terms: -1 + -9x + -3x2 = 1 + -1 + 9x + -9x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 -1 + -9x + -3x2 = 0 + 9x + -9x + 3x2 + -3x2 -1 + -9x + -3x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 -1 + -9x + -3x2 = 0 + 3x2 + -3x2 -1 + -9x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -1 + -9x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 9x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 9x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + 9x + 3x2 = 0 Solving 1 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 3x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 3x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 3x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 3x + x2 = 0 + -0.3333333333 3x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 3x + x2 = -0.3333333333 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 = -0.3333333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.3333333333 + 2.25 Combine like terms: -0.3333333333 + 2.25 = 1.9166666667 2.25 + 3x + x2 = 1.9166666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.9166666667 Calculate the square root of the right side: 1.38443731 Break this problem into two subproblems by setting (x + 1.5) equal to 1.38443731 and -1.38443731.Subproblem 1
x + 1.5 = 1.38443731 Simplifying x + 1.5 = 1.38443731 Reorder the terms: 1.5 + x = 1.38443731 Solving 1.5 + x = 1.38443731 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 = 1.38443731 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.38443731 + -1.5 x = 1.38443731 + -1.5 Combine like terms: 1.38443731 + -1.5 = -0.11556269 x = -0.11556269 Simplifying x = -0.11556269Subproblem 2
x + 1.5 = -1.38443731 Simplifying x + 1.5 = -1.38443731 Reorder the terms: 1.5 + x = -1.38443731 Solving 1.5 + x = -1.38443731 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 = -1.38443731 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.38443731 + -1.5 x = -1.38443731 + -1.5 Combine like terms: -1.38443731 + -1.5 = -2.88443731 x = -2.88443731 Simplifying x = -2.88443731Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.11556269, -2.88443731}Solution
x = {-0.11556269, -2.88443731}
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