24x^2+22x=4

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Solution for 24x^2+22x=4 equation:


Simplifying
24x2 + 22x = 4

Reorder the terms:
22x + 24x2 = 4

Solving
22x + 24x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 22x + 24x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 22x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 11x + 12x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + 11x + 12x2)' equal to zero and attempt to solve: Simplifying -2 + 11x + 12x2 = 0 Solving -2 + 11x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.1666666667 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.9166666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.9166666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.9166666667x + x2 = 0 + 0.1666666667 0.9166666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.9166666667x + x2 = 0.1666666667 The x term is 0.9166666667x. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667x + 0.2100694445 + x2 = 0.1666666667 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 0.1666666667 + 0.2100694445 Combine like terms: 0.1666666667 + 0.2100694445 = 0.3767361112 0.2100694445 + 0.9166666667x + x2 = 0.3767361112 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 0.3767361112 Calculate the square root of the right side: 0.613788328 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 0.613788328 and -0.613788328.

Subproblem 1

x + 0.4583333334 = 0.613788328 Simplifying x + 0.4583333334 = 0.613788328 Reorder the terms: 0.4583333334 + x = 0.613788328 Solving 0.4583333334 + x = 0.613788328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 0.613788328 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 0.613788328 + -0.4583333334 x = 0.613788328 + -0.4583333334 Combine like terms: 0.613788328 + -0.4583333334 = 0.1554549946 x = 0.1554549946 Simplifying x = 0.1554549946

Subproblem 2

x + 0.4583333334 = -0.613788328 Simplifying x + 0.4583333334 = -0.613788328 Reorder the terms: 0.4583333334 + x = -0.613788328 Solving 0.4583333334 + x = -0.613788328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -0.613788328 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -0.613788328 + -0.4583333334 x = -0.613788328 + -0.4583333334 Combine like terms: -0.613788328 + -0.4583333334 = -1.0721216614 x = -1.0721216614 Simplifying x = -1.0721216614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1554549946, -1.0721216614}

Solution

x = {0.1554549946, -1.0721216614}

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