10x^2-4x-250=0

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Solution for 10x^2-4x-250=0 equation:


Simplifying
10x2 + -4x + -250 = 0

Reorder the terms:
-250 + -4x + 10x2 = 0

Solving
-250 + -4x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + -2x + 5x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-125 + -2x + 5x2)' equal to zero and attempt to solve: Simplifying -125 + -2x + 5x2 = 0 Solving -125 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -25 + -0.4x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -0.4x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -0.4x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -0.4x + x2 = 0 + 25 -0.4x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -0.4x + x2 = 25 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 25 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 25 + 0.04 Combine like terms: 25 + 0.04 = 25.04 0.04 + -0.4x + x2 = 25.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 25.04 Calculate the square root of the right side: 5.003998401 Break this problem into two subproblems by setting (x + -0.2) equal to 5.003998401 and -5.003998401.

Subproblem 1

x + -0.2 = 5.003998401 Simplifying x + -0.2 = 5.003998401 Reorder the terms: -0.2 + x = 5.003998401 Solving -0.2 + x = 5.003998401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 5.003998401 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 5.003998401 + 0.2 x = 5.003998401 + 0.2 Combine like terms: 5.003998401 + 0.2 = 5.203998401 x = 5.203998401 Simplifying x = 5.203998401

Subproblem 2

x + -0.2 = -5.003998401 Simplifying x + -0.2 = -5.003998401 Reorder the terms: -0.2 + x = -5.003998401 Solving -0.2 + x = -5.003998401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -5.003998401 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -5.003998401 + 0.2 x = -5.003998401 + 0.2 Combine like terms: -5.003998401 + 0.2 = -4.803998401 x = -4.803998401 Simplifying x = -4.803998401

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.203998401, -4.803998401}

Solution

x = {5.203998401, -4.803998401}

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