24x^2+6x-8=0

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Solution for 24x^2+6x-8=0 equation:


Simplifying
24x2 + 6x + -8 = 0

Reorder the terms:
-8 + 6x + 24x2 = 0

Solving
-8 + 6x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3x + 12x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + 3x + 12x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + 12x2 = 0 Solving -4 + 3x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.3333333333 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.25x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.25x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.25x + x2 = 0 + 0.3333333333 0.25x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.25x + x2 = 0.3333333333 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.3333333333 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.3333333333 + 0.015625 Combine like terms: 0.3333333333 + 0.015625 = 0.3489583333 0.015625 + 0.25x + x2 = 0.3489583333 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.3489583333 Calculate the square root of the right side: 0.590726953 Break this problem into two subproblems by setting (x + 0.125) equal to 0.590726953 and -0.590726953.

Subproblem 1

x + 0.125 = 0.590726953 Simplifying x + 0.125 = 0.590726953 Reorder the terms: 0.125 + x = 0.590726953 Solving 0.125 + x = 0.590726953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.590726953 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.590726953 + -0.125 x = 0.590726953 + -0.125 Combine like terms: 0.590726953 + -0.125 = 0.465726953 x = 0.465726953 Simplifying x = 0.465726953

Subproblem 2

x + 0.125 = -0.590726953 Simplifying x + 0.125 = -0.590726953 Reorder the terms: 0.125 + x = -0.590726953 Solving 0.125 + x = -0.590726953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.590726953 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.590726953 + -0.125 x = -0.590726953 + -0.125 Combine like terms: -0.590726953 + -0.125 = -0.715726953 x = -0.715726953 Simplifying x = -0.715726953

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.465726953, -0.715726953}

Solution

x = {0.465726953, -0.715726953}

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