2400x^2+20x-4=0

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Solution for 2400x^2+20x-4=0 equation:


Simplifying
2400x2 + 20x + -4 = 0

Reorder the terms:
-4 + 20x + 2400x2 = 0

Solving
-4 + 20x + 2400x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 5x + 600x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-1 + 5x + 600x2)' equal to zero and attempt to solve: Simplifying -1 + 5x + 600x2 = 0 Solving -1 + 5x + 600x2 = 0 Begin completing the square. Divide all terms by 600 the coefficient of the squared term: Divide each side by '600'. -0.001666666667 + 0.008333333333x + x2 = 0.00 Move the constant term to the right: Add '0.001666666667' to each side of the equation. -0.001666666667 + 0.008333333333x + 0.001666666667 + x2 = 0.00 + 0.001666666667 Reorder the terms: -0.001666666667 + 0.001666666667 + 0.008333333333x + x2 = 0.00 + 0.001666666667 Combine like terms: -0.001666666667 + 0.001666666667 = 0.000000000000 0.000000000000 + 0.008333333333x + x2 = 0.00 + 0.001666666667 0.008333333333x + x2 = 0.00 + 0.001666666667 Combine like terms: 0.00 + 0.001666666667 = 0.001666666667 0.008333333333x + x2 = 0.001666666667 The x term is 0.008333333333x. Take half its coefficient (0.004166666667). Square it (0.00001736111111) and add it to both sides. Add '0.00001736111111' to each side of the equation. 0.008333333333x + 0.00001736111111 + x2 = 0.001666666667 + 0.00001736111111 Reorder the terms: 0.00001736111111 + 0.008333333333x + x2 = 0.001666666667 + 0.00001736111111 Combine like terms: 0.001666666667 + 0.00001736111111 = 0.00168402777811 0.00001736111111 + 0.008333333333x + x2 = 0.00168402777811 Factor a perfect square on the left side: (x + 0.004166666667)(x + 0.004166666667) = 0.00168402777811 Calculate the square root of the right side: 0.041036908 Break this problem into two subproblems by setting (x + 0.004166666667) equal to 0.041036908 and -0.041036908.

Subproblem 1

x + 0.004166666667 = 0.041036908 Simplifying x + 0.004166666667 = 0.041036908 Reorder the terms: 0.004166666667 + x = 0.041036908 Solving 0.004166666667 + x = 0.041036908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.004166666667' to each side of the equation. 0.004166666667 + -0.004166666667 + x = 0.041036908 + -0.004166666667 Combine like terms: 0.004166666667 + -0.004166666667 = 0.000000000000 0.000000000000 + x = 0.041036908 + -0.004166666667 x = 0.041036908 + -0.004166666667 Combine like terms: 0.041036908 + -0.004166666667 = 0.036870241333 x = 0.036870241333 Simplifying x = 0.036870241333

Subproblem 2

x + 0.004166666667 = -0.041036908 Simplifying x + 0.004166666667 = -0.041036908 Reorder the terms: 0.004166666667 + x = -0.041036908 Solving 0.004166666667 + x = -0.041036908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.004166666667' to each side of the equation. 0.004166666667 + -0.004166666667 + x = -0.041036908 + -0.004166666667 Combine like terms: 0.004166666667 + -0.004166666667 = 0.000000000000 0.000000000000 + x = -0.041036908 + -0.004166666667 x = -0.041036908 + -0.004166666667 Combine like terms: -0.041036908 + -0.004166666667 = -0.045203574667 x = -0.045203574667 Simplifying x = -0.045203574667

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.036870241333, -0.045203574667}

Solution

x = {0.036870241333, -0.045203574667}

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