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Simplifying 3x3 + -1x2 + -75x = 0 Reorder the terms: -75x + -1x2 + 3x3 = 0 Solving -75x + -1x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-75 + -1x + 3x2) = 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 '(-75 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -75 + -1x + 3x2 = 0 Solving -75 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -0.3333333333x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -0.3333333333x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -0.3333333333x + x2 = 0 + 25 -0.3333333333x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -0.3333333333x + x2 = 25 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 25 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 25 + 0.02777777779 Combine like terms: 25 + 0.02777777779 = 25.02777777779 0.02777777779 + -0.3333333333x + x2 = 25.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 25.02777777779 Calculate the square root of the right side: 5.002777007 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 5.002777007 and -5.002777007.Subproblem 1
x + -0.1666666667 = 5.002777007 Simplifying x + -0.1666666667 = 5.002777007 Reorder the terms: -0.1666666667 + x = 5.002777007 Solving -0.1666666667 + x = 5.002777007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 5.002777007 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 5.002777007 + 0.1666666667 x = 5.002777007 + 0.1666666667 Combine like terms: 5.002777007 + 0.1666666667 = 5.1694436737 x = 5.1694436737 Simplifying x = 5.1694436737Subproblem 2
x + -0.1666666667 = -5.002777007 Simplifying x + -0.1666666667 = -5.002777007 Reorder the terms: -0.1666666667 + x = -5.002777007 Solving -0.1666666667 + x = -5.002777007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -5.002777007 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -5.002777007 + 0.1666666667 x = -5.002777007 + 0.1666666667 Combine like terms: -5.002777007 + 0.1666666667 = -4.8361103403 x = -4.8361103403 Simplifying x = -4.8361103403Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1694436737, -4.8361103403}Solution
x = {0, 5.1694436737, -4.8361103403}
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