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Simplifying 6x3 + 44x2 + 15x = 0 Reorder the terms: 15x + 44x2 + 6x3 = 0 Solving 15x + 44x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(15 + 44x + 6x2) = 0Subproblem 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 '(15 + 44x + 6x2)' equal to zero and attempt to solve: Simplifying 15 + 44x + 6x2 = 0 Solving 15 + 44x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + 7.333333333x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 7.333333333x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 7.333333333x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 7.333333333x + x2 = 0 + -2.5 7.333333333x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 7.333333333x + x2 = -2.5 The x term is 7.333333333x. Take half its coefficient (3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. 7.333333333x + 13.44444445 + x2 = -2.5 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333x + x2 = -2.5 + 13.44444445 Combine like terms: -2.5 + 13.44444445 = 10.94444445 13.44444445 + 7.333333333x + x2 = 10.94444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 10.94444445 Calculate the square root of the right side: 3.308238874 Break this problem into two subproblems by setting (x + 3.666666667) equal to 3.308238874 and -3.308238874.Subproblem 1
x + 3.666666667 = 3.308238874 Simplifying x + 3.666666667 = 3.308238874 Reorder the terms: 3.666666667 + x = 3.308238874 Solving 3.666666667 + x = 3.308238874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = 3.308238874 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 3.308238874 + -3.666666667 x = 3.308238874 + -3.666666667 Combine like terms: 3.308238874 + -3.666666667 = -0.358427793 x = -0.358427793 Simplifying x = -0.358427793Subproblem 2
x + 3.666666667 = -3.308238874 Simplifying x + 3.666666667 = -3.308238874 Reorder the terms: 3.666666667 + x = -3.308238874 Solving 3.666666667 + x = -3.308238874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = -3.308238874 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -3.308238874 + -3.666666667 x = -3.308238874 + -3.666666667 Combine like terms: -3.308238874 + -3.666666667 = -6.974905541 x = -6.974905541 Simplifying x = -6.974905541Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.358427793, -6.974905541}Solution
x = {0, -0.358427793, -6.974905541}
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