(2x^2-5x-1)(x)=

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Solution for (2x^2-5x-1)(x)= equation:


Simplifying
(2x2 + -5x + -1)(x) = 0

Reorder the terms:
(-1 + -5x + 2x2)(x) = 0

Reorder the terms for easier multiplication:
x(-1 + -5x + 2x2) = 0
(-1 * x + -5x * x + 2x2 * x) = 0
(-1x + -5x2 + 2x3) = 0

Solving
-1x + -5x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + -5x + 2x2) = 0

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 = 0

Subproblem 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 = 2.686140662

Subproblem 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 = -0.186140662

Solution

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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