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Simplifying 72x3 + 6x2 + -444x = 0 Reorder the terms: -444x + 6x2 + 72x3 = 0 Solving -444x + 6x2 + 72x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-74 + x + 12x2) = 0 Ignore the factor 6.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 '(-74 + x + 12x2)' equal to zero and attempt to solve: Simplifying -74 + x + 12x2 = 0 Solving -74 + x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -6.166666667 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '6.166666667' to each side of the equation. -6.166666667 + 0.08333333333x + 6.166666667 + x2 = 0 + 6.166666667 Reorder the terms: -6.166666667 + 6.166666667 + 0.08333333333x + x2 = 0 + 6.166666667 Combine like terms: -6.166666667 + 6.166666667 = 0.000000000 0.000000000 + 0.08333333333x + x2 = 0 + 6.166666667 0.08333333333x + x2 = 0 + 6.166666667 Combine like terms: 0 + 6.166666667 = 6.166666667 0.08333333333x + x2 = 6.166666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.08333333333x + 0.25 + x2 = 6.166666667 + 0.25 Reorder the terms: 0.25 + 0.08333333333x + x2 = 6.166666667 + 0.25 Combine like terms: 6.166666667 + 0.25 = 6.416666667 0.25 + 0.08333333333x + x2 = 6.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6.416666667 Calculate the square root of the right side: 2.533114026 Break this problem into two subproblems by setting (x + 0.5) equal to 2.533114026 and -2.533114026.Subproblem 1
x + 0.5 = 2.533114026 Simplifying x + 0.5 = 2.533114026 Reorder the terms: 0.5 + x = 2.533114026 Solving 0.5 + x = 2.533114026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.533114026 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.533114026 + -0.5 x = 2.533114026 + -0.5 Combine like terms: 2.533114026 + -0.5 = 2.033114026 x = 2.033114026 Simplifying x = 2.033114026Subproblem 2
x + 0.5 = -2.533114026 Simplifying x + 0.5 = -2.533114026 Reorder the terms: 0.5 + x = -2.533114026 Solving 0.5 + x = -2.533114026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.533114026 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.533114026 + -0.5 x = -2.533114026 + -0.5 Combine like terms: -2.533114026 + -0.5 = -3.033114026 x = -3.033114026 Simplifying x = -3.033114026Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.033114026, -3.033114026}Solution
x = {0, 2.033114026, -3.033114026}
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