4(9x^2+x-355)=0

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Solution for 4(9x^2+x-355)=0 equation:


Simplifying
4(9x2 + x + -355) = 0

Reorder the terms:
4(-355 + x + 9x2) = 0
(-355 * 4 + x * 4 + 9x2 * 4) = 0
(-1420 + 4x + 36x2) = 0

Solving
-1420 + 4x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-355 + x + 9x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-355 + x + 9x2)' equal to zero and attempt to solve: Simplifying -355 + x + 9x2 = 0 Solving -355 + x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -39.44444444 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '39.44444444' to each side of the equation. -39.44444444 + 0.1111111111x + 39.44444444 + x2 = 0 + 39.44444444 Reorder the terms: -39.44444444 + 39.44444444 + 0.1111111111x + x2 = 0 + 39.44444444 Combine like terms: -39.44444444 + 39.44444444 = 0.00000000 0.00000000 + 0.1111111111x + x2 = 0 + 39.44444444 0.1111111111x + x2 = 0 + 39.44444444 Combine like terms: 0 + 39.44444444 = 39.44444444 0.1111111111x + x2 = 39.44444444 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x + 0.25 + x2 = 39.44444444 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = 39.44444444 + 0.25 Combine like terms: 39.44444444 + 0.25 = 39.69444444 0.25 + 0.1111111111x + x2 = 39.69444444 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 39.69444444 Calculate the square root of the right side: 6.300352723 Break this problem into two subproblems by setting (x + 0.5) equal to 6.300352723 and -6.300352723.

Subproblem 1

x + 0.5 = 6.300352723 Simplifying x + 0.5 = 6.300352723 Reorder the terms: 0.5 + x = 6.300352723 Solving 0.5 + x = 6.300352723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.300352723 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.300352723 + -0.5 x = 6.300352723 + -0.5 Combine like terms: 6.300352723 + -0.5 = 5.800352723 x = 5.800352723 Simplifying x = 5.800352723

Subproblem 2

x + 0.5 = -6.300352723 Simplifying x + 0.5 = -6.300352723 Reorder the terms: 0.5 + x = -6.300352723 Solving 0.5 + x = -6.300352723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.300352723 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.300352723 + -0.5 x = -6.300352723 + -0.5 Combine like terms: -6.300352723 + -0.5 = -6.800352723 x = -6.800352723 Simplifying x = -6.800352723

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.800352723, -6.800352723}

Solution

x = {5.800352723, -6.800352723}

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