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Simplifying 0 = ((-5x + -1) + (2x2)) * x Reorder the terms: 0 = ((-1 + -5x) + (2x2)) * x Remove parenthesis around (-1 + -5x) 0 = (-1 + -5x + (2x2)) * x Reorder the terms for easier multiplication: 0 = x(-1 + -5x + (2x2)) 0 = (-1 * x + -5x * x + (2x2) * x) 0 = (-1x + -5x2 + 2x3) Solving 0 = -1x + -5x2 + 2x3 Solving for variable 'x'. Remove the zero: x + 5x2 + -2x3 = -1x + -5x2 + 2x3 + x + 5x2 + -2x3 Reorder the terms: x + 5x2 + -2x3 = -1x + x + -5x2 + 5x2 + 2x3 + -2x3 Combine like terms: -1x + x = 0 x + 5x2 + -2x3 = 0 + -5x2 + 5x2 + 2x3 + -2x3 x + 5x2 + -2x3 = -5x2 + 5x2 + 2x3 + -2x3 Combine like terms: -5x2 + 5x2 = 0 x + 5x2 + -2x3 = 0 + 2x3 + -2x3 x + 5x2 + -2x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 x + 5x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 5x + -2x2) = 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 '(1 + 5x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + -2x2 = 0 Solving 1 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.5x + x2 = 0 + 0.5 -2.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.5x + x2 = 0.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.5 + 1.5625 Combine like terms: 0.5 + 1.5625 = 2.0625 1.5625 + -2.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + -1.25) equal to 1.436140662 and -1.436140662.Subproblem 1
x + -1.25 = 1.436140662 Simplifying x + -1.25 = 1.436140662 Reorder the terms: -1.25 + x = 1.436140662 Solving -1.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.436140662 + 1.25 x = 1.436140662 + 1.25 Combine like terms: 1.436140662 + 1.25 = 2.686140662 x = 2.686140662 Simplifying x = 2.686140662Subproblem 2
x + -1.25 = -1.436140662 Simplifying x + -1.25 = -1.436140662 Reorder the terms: -1.25 + x = -1.436140662 Solving -1.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.436140662 + 1.25 x = -1.436140662 + 1.25 Combine like terms: -1.436140662 + 1.25 = -0.186140662 x = -0.186140662 Simplifying x = -0.186140662Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.686140662, -0.186140662}Solution
x = {0, 2.686140662, -0.186140662}
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