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Simplifying 91x3 + -633x2 + -182x = 0 Reorder the terms: -182x + -633x2 + 91x3 = 0 Solving -182x + -633x2 + 91x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-182 + -633x + 91x2) = 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 '(-182 + -633x + 91x2)' equal to zero and attempt to solve: Simplifying -182 + -633x + 91x2 = 0 Solving -182 + -633x + 91x2 = 0 Begin completing the square. Divide all terms by 91 the coefficient of the squared term: Divide each side by '91'. -2 + -6.956043956x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6.956043956x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -6.956043956x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6.956043956x + x2 = 0 + 2 -6.956043956x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6.956043956x + x2 = 2 The x term is -6.956043956x. Take half its coefficient (-3.478021978). Square it (12.09663688) and add it to both sides. Add '12.09663688' to each side of the equation. -6.956043956x + 12.09663688 + x2 = 2 + 12.09663688 Reorder the terms: 12.09663688 + -6.956043956x + x2 = 2 + 12.09663688 Combine like terms: 2 + 12.09663688 = 14.09663688 12.09663688 + -6.956043956x + x2 = 14.09663688 Factor a perfect square on the left side: (x + -3.478021978)(x + -3.478021978) = 14.09663688 Calculate the square root of the right side: 3.754548825 Break this problem into two subproblems by setting (x + -3.478021978) equal to 3.754548825 and -3.754548825.Subproblem 1
x + -3.478021978 = 3.754548825 Simplifying x + -3.478021978 = 3.754548825 Reorder the terms: -3.478021978 + x = 3.754548825 Solving -3.478021978 + x = 3.754548825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.478021978' to each side of the equation. -3.478021978 + 3.478021978 + x = 3.754548825 + 3.478021978 Combine like terms: -3.478021978 + 3.478021978 = 0.000000000 0.000000000 + x = 3.754548825 + 3.478021978 x = 3.754548825 + 3.478021978 Combine like terms: 3.754548825 + 3.478021978 = 7.232570803 x = 7.232570803 Simplifying x = 7.232570803Subproblem 2
x + -3.478021978 = -3.754548825 Simplifying x + -3.478021978 = -3.754548825 Reorder the terms: -3.478021978 + x = -3.754548825 Solving -3.478021978 + x = -3.754548825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.478021978' to each side of the equation. -3.478021978 + 3.478021978 + x = -3.754548825 + 3.478021978 Combine like terms: -3.478021978 + 3.478021978 = 0.000000000 0.000000000 + x = -3.754548825 + 3.478021978 x = -3.754548825 + 3.478021978 Combine like terms: -3.754548825 + 3.478021978 = -0.276526847 x = -0.276526847 Simplifying x = -0.276526847Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.232570803, -0.276526847}Solution
x = {0, 7.232570803, -0.276526847}
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