0=24+36x-4.9x^2

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Solution for 0=24+36x-4.9x^2 equation:


Simplifying
0 = 24 + 36x + -4.9x2

Solving
0 = 24 + 36x + -4.9x2

Solving for variable 'x'.

Combine like terms: 0 + -24 = -24
-24 + -36x + 4.9x2 = 24 + 36x + -4.9x2 + -24 + -36x + 4.9x2

Reorder the terms:
-24 + -36x + 4.9x2 = 24 + -24 + 36x + -36x + -4.9x2 + 4.9x2

Combine like terms: 24 + -24 = 0
-24 + -36x + 4.9x2 = 0 + 36x + -36x + -4.9x2 + 4.9x2
-24 + -36x + 4.9x2 = 36x + -36x + -4.9x2 + 4.9x2

Combine like terms: 36x + -36x = 0
-24 + -36x + 4.9x2 = 0 + -4.9x2 + 4.9x2
-24 + -36x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-24 + -36x + 4.9x2 = 0.0

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

Divide each side by '4.9'.
-4.897959184 + -7.346938776x + x2 = 0

Move the constant term to the right:

Add '4.897959184' to each side of the equation.
-4.897959184 + -7.346938776x + 4.897959184 + x2 = 0 + 4.897959184

Reorder the terms:
-4.897959184 + 4.897959184 + -7.346938776x + x2 = 0 + 4.897959184

Combine like terms: -4.897959184 + 4.897959184 = 0.000000000
0.000000000 + -7.346938776x + x2 = 0 + 4.897959184
-7.346938776x + x2 = 0 + 4.897959184

Combine like terms: 0 + 4.897959184 = 4.897959184
-7.346938776x + x2 = 4.897959184

The x term is -7.346938776x.  Take half its coefficient (-3.673469388).
Square it (13.49437734) and add it to both sides.

Add '13.49437734' to each side of the equation.
-7.346938776x + 13.49437734 + x2 = 4.897959184 + 13.49437734

Reorder the terms:
13.49437734 + -7.346938776x + x2 = 4.897959184 + 13.49437734

Combine like terms: 4.897959184 + 13.49437734 = 18.392336524
13.49437734 + -7.346938776x + x2 = 18.392336524

Factor a perfect square on the left side:
(x + -3.673469388)(x + -3.673469388) = 18.392336524

Calculate the square root of the right side: 4.288628746

Break this problem into two subproblems by setting 
(x + -3.673469388) equal to 4.288628746 and -4.288628746.

Subproblem 1

x + -3.673469388 = 4.288628746 Simplifying x + -3.673469388 = 4.288628746 Reorder the terms: -3.673469388 + x = 4.288628746 Solving -3.673469388 + x = 4.288628746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.673469388' to each side of the equation. -3.673469388 + 3.673469388 + x = 4.288628746 + 3.673469388 Combine like terms: -3.673469388 + 3.673469388 = 0.000000000 0.000000000 + x = 4.288628746 + 3.673469388 x = 4.288628746 + 3.673469388 Combine like terms: 4.288628746 + 3.673469388 = 7.962098134 x = 7.962098134 Simplifying x = 7.962098134

Subproblem 2

x + -3.673469388 = -4.288628746 Simplifying x + -3.673469388 = -4.288628746 Reorder the terms: -3.673469388 + x = -4.288628746 Solving -3.673469388 + x = -4.288628746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.673469388' to each side of the equation. -3.673469388 + 3.673469388 + x = -4.288628746 + 3.673469388 Combine like terms: -3.673469388 + 3.673469388 = 0.000000000 0.000000000 + x = -4.288628746 + 3.673469388 x = -4.288628746 + 3.673469388 Combine like terms: -4.288628746 + 3.673469388 = -0.615159358 x = -0.615159358 Simplifying x = -0.615159358

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.962098134, -0.615159358}

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