20x^2+224x-3840=0

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Solution for 20x^2+224x-3840=0 equation:


Simplifying
20x2 + 224x + -3840 = 0

Reorder the terms:
-3840 + 224x + 20x2 = 0

Solving
-3840 + 224x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-960 + 56x + 5x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-960 + 56x + 5x2)' equal to zero and attempt to solve: Simplifying -960 + 56x + 5x2 = 0 Solving -960 + 56x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -192 + 11.2x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 11.2x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 11.2x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 11.2x + x2 = 0 + 192 11.2x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 11.2x + x2 = 192 The x term is 11.2x. Take half its coefficient (5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. 11.2x + 31.36 + x2 = 192 + 31.36 Reorder the terms: 31.36 + 11.2x + x2 = 192 + 31.36 Combine like terms: 192 + 31.36 = 223.36 31.36 + 11.2x + x2 = 223.36 Factor a perfect square on the left side: (x + 5.6)(x + 5.6) = 223.36 Calculate the square root of the right side: 14.945233354 Break this problem into two subproblems by setting (x + 5.6) equal to 14.945233354 and -14.945233354.

Subproblem 1

x + 5.6 = 14.945233354 Simplifying x + 5.6 = 14.945233354 Reorder the terms: 5.6 + x = 14.945233354 Solving 5.6 + x = 14.945233354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = 14.945233354 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = 14.945233354 + -5.6 x = 14.945233354 + -5.6 Combine like terms: 14.945233354 + -5.6 = 9.345233354 x = 9.345233354 Simplifying x = 9.345233354

Subproblem 2

x + 5.6 = -14.945233354 Simplifying x + 5.6 = -14.945233354 Reorder the terms: 5.6 + x = -14.945233354 Solving 5.6 + x = -14.945233354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = -14.945233354 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = -14.945233354 + -5.6 x = -14.945233354 + -5.6 Combine like terms: -14.945233354 + -5.6 = -20.545233354 x = -20.545233354 Simplifying x = -20.545233354

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.345233354, -20.545233354}

Solution

x = {9.345233354, -20.545233354}

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