4.9x^2+24x-13=0

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Solution for 4.9x^2+24x-13=0 equation:


Simplifying
4.9x2 + 24x + -13 = 0

Reorder the terms:
-13 + 24x + 4.9x2 = 0

Solving
-13 + 24x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
-2.653061224 + 4.897959184x + x2 = 0

Move the constant term to the right:

Add '2.653061224' to each side of the equation.
-2.653061224 + 4.897959184x + 2.653061224 + x2 = 0 + 2.653061224

Reorder the terms:
-2.653061224 + 2.653061224 + 4.897959184x + x2 = 0 + 2.653061224

Combine like terms: -2.653061224 + 2.653061224 = 0.000000000
0.000000000 + 4.897959184x + x2 = 0 + 2.653061224
4.897959184x + x2 = 0 + 2.653061224

Combine like terms: 0 + 2.653061224 = 2.653061224
4.897959184x + x2 = 2.653061224

The x term is 4.897959184x.  Take half its coefficient (2.448979592).
Square it (5.997501042) and add it to both sides.

Add '5.997501042' to each side of the equation.
4.897959184x + 5.997501042 + x2 = 2.653061224 + 5.997501042

Reorder the terms:
5.997501042 + 4.897959184x + x2 = 2.653061224 + 5.997501042

Combine like terms: 2.653061224 + 5.997501042 = 8.650562266
5.997501042 + 4.897959184x + x2 = 8.650562266

Factor a perfect square on the left side:
(x + 2.448979592)(x + 2.448979592) = 8.650562266

Calculate the square root of the right side: 2.941183821

Break this problem into two subproblems by setting 
(x + 2.448979592) equal to 2.941183821 and -2.941183821.

Subproblem 1

x + 2.448979592 = 2.941183821 Simplifying x + 2.448979592 = 2.941183821 Reorder the terms: 2.448979592 + x = 2.941183821 Solving 2.448979592 + x = 2.941183821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.448979592' to each side of the equation. 2.448979592 + -2.448979592 + x = 2.941183821 + -2.448979592 Combine like terms: 2.448979592 + -2.448979592 = 0.000000000 0.000000000 + x = 2.941183821 + -2.448979592 x = 2.941183821 + -2.448979592 Combine like terms: 2.941183821 + -2.448979592 = 0.492204229 x = 0.492204229 Simplifying x = 0.492204229

Subproblem 2

x + 2.448979592 = -2.941183821 Simplifying x + 2.448979592 = -2.941183821 Reorder the terms: 2.448979592 + x = -2.941183821 Solving 2.448979592 + x = -2.941183821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.448979592' to each side of the equation. 2.448979592 + -2.448979592 + x = -2.941183821 + -2.448979592 Combine like terms: 2.448979592 + -2.448979592 = 0.000000000 0.000000000 + x = -2.941183821 + -2.448979592 x = -2.941183821 + -2.448979592 Combine like terms: -2.941183821 + -2.448979592 = -5.390163413 x = -5.390163413 Simplifying x = -5.390163413

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.492204229, -5.390163413}

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