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Simplifying 11x2 + -5x + 7x3 = 0 Reorder the terms: -5x + 11x2 + 7x3 = 0 Solving -5x + 11x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 11x + 7x2) = 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 '(-5 + 11x + 7x2)' equal to zero and attempt to solve: Simplifying -5 + 11x + 7x2 = 0 Solving -5 + 11x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 1.571428571x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 1.571428571x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 1.571428571x + x2 = 0 + 0.7142857143 1.571428571x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 1.571428571x + x2 = 0.7142857143 The x term is 1.571428571x. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x + 0.6173469384 + x2 = 0.7142857143 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = 0.7142857143 + 0.6173469384 Combine like terms: 0.7142857143 + 0.6173469384 = 1.3316326527 0.6173469384 + 1.571428571x + x2 = 1.3316326527 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 1.3316326527 Calculate the square root of the right side: 1.153963887 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 1.153963887 and -1.153963887.Subproblem 1
x + 0.7857142855 = 1.153963887 Simplifying x + 0.7857142855 = 1.153963887 Reorder the terms: 0.7857142855 + x = 1.153963887 Solving 0.7857142855 + x = 1.153963887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 1.153963887 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 1.153963887 + -0.7857142855 x = 1.153963887 + -0.7857142855 Combine like terms: 1.153963887 + -0.7857142855 = 0.3682496015 x = 0.3682496015 Simplifying x = 0.3682496015Subproblem 2
x + 0.7857142855 = -1.153963887 Simplifying x + 0.7857142855 = -1.153963887 Reorder the terms: 0.7857142855 + x = -1.153963887 Solving 0.7857142855 + x = -1.153963887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -1.153963887 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -1.153963887 + -0.7857142855 x = -1.153963887 + -0.7857142855 Combine like terms: -1.153963887 + -0.7857142855 = -1.9396781725 x = -1.9396781725 Simplifying x = -1.9396781725Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3682496015, -1.9396781725}Solution
x = {0, 0.3682496015, -1.9396781725}
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