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Simplifying -44x3 + -28x2 + 12x = 0 Reorder the terms: 12x + -28x2 + -44x3 = 0 Solving 12x + -28x2 + -44x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(3 + -7x + -11x2) = 0 Ignore the factor 4.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 + -7x + -11x2)' equal to zero and attempt to solve: Simplifying 3 + -7x + -11x2 = 0 Solving 3 + -7x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.2727272727 + 0.6363636364x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + 0.6363636364x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + 0.6363636364x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + 0.6363636364x + x2 = 0 + 0.2727272727 0.6363636364x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 0.6363636364x + x2 = 0.2727272727 The x term is 0.6363636364x. Take half its coefficient (0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. 0.6363636364x + 0.1012396694 + x2 = 0.2727272727 + 0.1012396694 Reorder the terms: 0.1012396694 + 0.6363636364x + x2 = 0.2727272727 + 0.1012396694 Combine like terms: 0.2727272727 + 0.1012396694 = 0.3739669421 0.1012396694 + 0.6363636364x + x2 = 0.3739669421 Factor a perfect square on the left side: (x + 0.3181818182)(x + 0.3181818182) = 0.3739669421 Calculate the square root of the right side: 0.611528366 Break this problem into two subproblems by setting (x + 0.3181818182) equal to 0.611528366 and -0.611528366.Subproblem 1
x + 0.3181818182 = 0.611528366 Simplifying x + 0.3181818182 = 0.611528366 Reorder the terms: 0.3181818182 + x = 0.611528366 Solving 0.3181818182 + x = 0.611528366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + x = 0.611528366 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = 0.611528366 + -0.3181818182 x = 0.611528366 + -0.3181818182 Combine like terms: 0.611528366 + -0.3181818182 = 0.2933465478 x = 0.2933465478 Simplifying x = 0.2933465478Subproblem 2
x + 0.3181818182 = -0.611528366 Simplifying x + 0.3181818182 = -0.611528366 Reorder the terms: 0.3181818182 + x = -0.611528366 Solving 0.3181818182 + x = -0.611528366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + x = -0.611528366 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = -0.611528366 + -0.3181818182 x = -0.611528366 + -0.3181818182 Combine like terms: -0.611528366 + -0.3181818182 = -0.9297101842 x = -0.9297101842 Simplifying x = -0.9297101842Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2933465478, -0.9297101842}Solution
x = {0, 0.2933465478, -0.9297101842}
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