2x^2-20x+124=76000000000

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Solution for 2x^2-20x+124=76000000000 equation:


Simplifying
2x2 + -20x + 124 = 76000000000

Reorder the terms:
124 + -20x + 2x2 = 76000000000

Solving
124 + -20x + 2x2 = 76000000000

Solving for variable 'x'.

Reorder the terms:
124 + -76000000000 + -20x + 2x2 = 76000000000 + -76000000000

Combine like terms: 124 + -76000000000 = -75999999876
-75999999876 + -20x + 2x2 = 76000000000 + -76000000000

Combine like terms: 76000000000 + -76000000000 = 0
-75999999876 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-37999999940 + -10x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-37999999940 + -10x + x2)' equal to zero and attempt to solve: Simplifying -37999999940 + -10x + x2 = 0 Solving -37999999940 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37999999940' to each side of the equation. -37999999940 + -10x + 37999999940 + x2 = 0 + 37999999940 Reorder the terms: -37999999940 + 37999999940 + -10x + x2 = 0 + 37999999940 Combine like terms: -37999999940 + 37999999940 = 0 0 + -10x + x2 = 0 + 37999999940 -10x + x2 = 0 + 37999999940 Combine like terms: 0 + 37999999940 = 37999999940 -10x + x2 = 37999999940 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 37999999940 + 25 Reorder the terms: 25 + -10x + x2 = 37999999940 + 25 Combine like terms: 37999999940 + 25 = 37999999965 25 + -10x + x2 = 37999999965 Factor a perfect square on the left side: (x + -5)(x + -5) = 37999999965 Calculate the square root of the right side: 194935.886806406 Break this problem into two subproblems by setting (x + -5) equal to 194935.886806406 and -194935.886806406.

Subproblem 1

x + -5 = 194935.886806406 Simplifying x + -5 = 194935.886806406 Reorder the terms: -5 + x = 194935.886806406 Solving -5 + x = 194935.886806406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 194935.886806406 + 5 Combine like terms: -5 + 5 = 0 0 + x = 194935.886806406 + 5 x = 194935.886806406 + 5 Combine like terms: 194935.886806406 + 5 = 194940.886806406 x = 194940.886806406 Simplifying x = 194940.886806406

Subproblem 2

x + -5 = -194935.886806406 Simplifying x + -5 = -194935.886806406 Reorder the terms: -5 + x = -194935.886806406 Solving -5 + x = -194935.886806406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -194935.886806406 + 5 Combine like terms: -5 + 5 = 0 0 + x = -194935.886806406 + 5 x = -194935.886806406 + 5 Combine like terms: -194935.886806406 + 5 = -194930.886806406 x = -194930.886806406 Simplifying x = -194930.886806406

Solution

The solution to the problem is based on the solutions from the subproblems. x = {194940.886806406, -194930.886806406}

Solution

x = {194940.886806406, -194930.886806406}

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