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Simplifying 18x3 + 16x2 + -6x = 0 Reorder the terms: -6x + 16x2 + 18x3 = 0 Solving -6x + 16x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + 8x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-3 + 8x + 9x2)' equal to zero and attempt to solve: Simplifying -3 + 8x + 9x2 = 0 Solving -3 + 8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.8888888889x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.8888888889x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.8888888889x + x2 = 0 + 0.3333333333 0.8888888889x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.8888888889x + x2 = 0.3333333333 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 0.3333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 0.3333333333 + 0.1975308642 Combine like terms: 0.3333333333 + 0.1975308642 = 0.5308641975 0.1975308642 + 0.8888888889x + x2 = 0.5308641975 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 0.5308641975 Calculate the square root of the right side: 0.72860428 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 0.72860428 and -0.72860428.Subproblem 1
x + 0.4444444445 = 0.72860428 Simplifying x + 0.4444444445 = 0.72860428 Reorder the terms: 0.4444444445 + x = 0.72860428 Solving 0.4444444445 + x = 0.72860428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 0.72860428 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 0.72860428 + -0.4444444445 x = 0.72860428 + -0.4444444445 Combine like terms: 0.72860428 + -0.4444444445 = 0.2841598355 x = 0.2841598355 Simplifying x = 0.2841598355Subproblem 2
x + 0.4444444445 = -0.72860428 Simplifying x + 0.4444444445 = -0.72860428 Reorder the terms: 0.4444444445 + x = -0.72860428 Solving 0.4444444445 + x = -0.72860428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -0.72860428 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -0.72860428 + -0.4444444445 x = -0.72860428 + -0.4444444445 Combine like terms: -0.72860428 + -0.4444444445 = -1.1730487245 x = -1.1730487245 Simplifying x = -1.1730487245Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2841598355, -1.1730487245}Solution
x = {0, 0.2841598355, -1.1730487245}
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