50x^2-300x-275=0

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Solution for 50x^2-300x-275=0 equation:


Simplifying
50x2 + -300x + -275 = 0

Reorder the terms:
-275 + -300x + 50x2 = 0

Solving
-275 + -300x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25'.
25(-11 + -12x + 2x2) = 0

Ignore the factor 25.

Subproblem 1

Set the factor '(-11 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying -11 + -12x + 2x2 = 0 Solving -11 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -6x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -6x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -6x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -6x + x2 = 0 + 5.5 -6x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -6x + x2 = 5.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 5.5 + 9 Reorder the terms: 9 + -6x + x2 = 5.5 + 9 Combine like terms: 5.5 + 9 = 14.5 9 + -6x + x2 = 14.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (x + -3) equal to 3.807886553 and -3.807886553.

Subproblem 1

x + -3 = 3.807886553 Simplifying x + -3 = 3.807886553 Reorder the terms: -3 + x = 3.807886553 Solving -3 + x = 3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.807886553 + 3 x = 3.807886553 + 3 Combine like terms: 3.807886553 + 3 = 6.807886553 x = 6.807886553 Simplifying x = 6.807886553

Subproblem 2

x + -3 = -3.807886553 Simplifying x + -3 = -3.807886553 Reorder the terms: -3 + x = -3.807886553 Solving -3 + x = -3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.807886553 + 3 x = -3.807886553 + 3 Combine like terms: -3.807886553 + 3 = -0.807886553 x = -0.807886553 Simplifying x = -0.807886553

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.807886553, -0.807886553}

Solution

x = {6.807886553, -0.807886553}

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