5x^2-24x-28=0

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Solution for 5x^2-24x-28=0 equation:


Simplifying
5x2 + -24x + -28 = 0

Reorder the terms:
-28 + -24x + 5x2 = 0

Solving
-28 + -24x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-5.6 + -4.8x + x2 = 0

Move the constant term to the right:

Add '5.6' to each side of the equation.
-5.6 + -4.8x + 5.6 + x2 = 0 + 5.6

Reorder the terms:
-5.6 + 5.6 + -4.8x + x2 = 0 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + -4.8x + x2 = 0 + 5.6
-4.8x + x2 = 0 + 5.6

Combine like terms: 0 + 5.6 = 5.6
-4.8x + x2 = 5.6

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = 5.6 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = 5.6 + 5.76

Combine like terms: 5.6 + 5.76 = 11.36
5.76 + -4.8x + x2 = 11.36

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 11.36

Calculate the square root of the right side: 3.370459909

Break this problem into two subproblems by setting 
(x + -2.4) equal to 3.370459909 and -3.370459909.

Subproblem 1

x + -2.4 = 3.370459909 Simplifying x + -2.4 = 3.370459909 Reorder the terms: -2.4 + x = 3.370459909 Solving -2.4 + x = 3.370459909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 3.370459909 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 3.370459909 + 2.4 x = 3.370459909 + 2.4 Combine like terms: 3.370459909 + 2.4 = 5.770459909 x = 5.770459909 Simplifying x = 5.770459909

Subproblem 2

x + -2.4 = -3.370459909 Simplifying x + -2.4 = -3.370459909 Reorder the terms: -2.4 + x = -3.370459909 Solving -2.4 + x = -3.370459909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -3.370459909 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -3.370459909 + 2.4 x = -3.370459909 + 2.4 Combine like terms: -3.370459909 + 2.4 = -0.970459909 x = -0.970459909 Simplifying x = -0.970459909

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.770459909, -0.970459909}

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