48x^2+58x+8=0

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Solution for 48x^2+58x+8=0 equation:


Simplifying
48x2 + 58x + 8 = 0

Reorder the terms:
8 + 58x + 48x2 = 0

Solving
8 + 58x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 29x + 24x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(4 + 29x + 24x2)' equal to zero and attempt to solve: Simplifying 4 + 29x + 24x2 = 0 Solving 4 + 29x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.1666666667 + 1.208333333x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 1.208333333x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 1.208333333x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 1.208333333x + x2 = 0 + -0.1666666667 1.208333333x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 1.208333333x + x2 = -0.1666666667 The x term is 1.208333333x. Take half its coefficient (0.6041666665). Square it (0.3650173609) and add it to both sides. Add '0.3650173609' to each side of the equation. 1.208333333x + 0.3650173609 + x2 = -0.1666666667 + 0.3650173609 Reorder the terms: 0.3650173609 + 1.208333333x + x2 = -0.1666666667 + 0.3650173609 Combine like terms: -0.1666666667 + 0.3650173609 = 0.1983506942 0.3650173609 + 1.208333333x + x2 = 0.1983506942 Factor a perfect square on the left side: (x + 0.6041666665)(x + 0.6041666665) = 0.1983506942 Calculate the square root of the right side: 0.445365798 Break this problem into two subproblems by setting (x + 0.6041666665) equal to 0.445365798 and -0.445365798.

Subproblem 1

x + 0.6041666665 = 0.445365798 Simplifying x + 0.6041666665 = 0.445365798 Reorder the terms: 0.6041666665 + x = 0.445365798 Solving 0.6041666665 + x = 0.445365798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6041666665' to each side of the equation. 0.6041666665 + -0.6041666665 + x = 0.445365798 + -0.6041666665 Combine like terms: 0.6041666665 + -0.6041666665 = 0.0000000000 0.0000000000 + x = 0.445365798 + -0.6041666665 x = 0.445365798 + -0.6041666665 Combine like terms: 0.445365798 + -0.6041666665 = -0.1588008685 x = -0.1588008685 Simplifying x = -0.1588008685

Subproblem 2

x + 0.6041666665 = -0.445365798 Simplifying x + 0.6041666665 = -0.445365798 Reorder the terms: 0.6041666665 + x = -0.445365798 Solving 0.6041666665 + x = -0.445365798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6041666665' to each side of the equation. 0.6041666665 + -0.6041666665 + x = -0.445365798 + -0.6041666665 Combine like terms: 0.6041666665 + -0.6041666665 = 0.0000000000 0.0000000000 + x = -0.445365798 + -0.6041666665 x = -0.445365798 + -0.6041666665 Combine like terms: -0.445365798 + -0.6041666665 = -1.0495324645 x = -1.0495324645 Simplifying x = -1.0495324645

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.1588008685, -1.0495324645}

Solution

x = {-0.1588008685, -1.0495324645}

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