0=-4.9x^2+12x+69

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Solution for 0=-4.9x^2+12x+69 equation:


Simplifying
0 = -4.9x2 + 12x + 69

Reorder the terms:
0 = 69 + 12x + -4.9x2

Solving
0 = 69 + 12x + -4.9x2

Solving for variable 'x'.

Combine like terms: 0 + -69 = -69
-69 + -12x + 4.9x2 = 69 + 12x + -4.9x2 + -69 + -12x + 4.9x2

Reorder the terms:
-69 + -12x + 4.9x2 = 69 + -69 + 12x + -12x + -4.9x2 + 4.9x2

Combine like terms: 69 + -69 = 0
-69 + -12x + 4.9x2 = 0 + 12x + -12x + -4.9x2 + 4.9x2
-69 + -12x + 4.9x2 = 12x + -12x + -4.9x2 + 4.9x2

Combine like terms: 12x + -12x = 0
-69 + -12x + 4.9x2 = 0 + -4.9x2 + 4.9x2
-69 + -12x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-69 + -12x + 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'.
-14.08163265 + -2.448979592x + x2 = 0

Move the constant term to the right:

Add '14.08163265' to each side of the equation.
-14.08163265 + -2.448979592x + 14.08163265 + x2 = 0 + 14.08163265

Reorder the terms:
-14.08163265 + 14.08163265 + -2.448979592x + x2 = 0 + 14.08163265

Combine like terms: -14.08163265 + 14.08163265 = 0.00000000
0.00000000 + -2.448979592x + x2 = 0 + 14.08163265
-2.448979592x + x2 = 0 + 14.08163265

Combine like terms: 0 + 14.08163265 = 14.08163265
-2.448979592x + x2 = 14.08163265

The x term is -2.448979592x.  Take half its coefficient (-1.224489796).
Square it (1.499375261) and add it to both sides.

Add '1.499375261' to each side of the equation.
-2.448979592x + 1.499375261 + x2 = 14.08163265 + 1.499375261

Reorder the terms:
1.499375261 + -2.448979592x + x2 = 14.08163265 + 1.499375261

Combine like terms: 14.08163265 + 1.499375261 = 15.581007911
1.499375261 + -2.448979592x + x2 = 15.581007911

Factor a perfect square on the left side:
(x + -1.224489796)(x + -1.224489796) = 15.581007911

Calculate the square root of the right side: 3.947278545

Break this problem into two subproblems by setting 
(x + -1.224489796) equal to 3.947278545 and -3.947278545.

Subproblem 1

x + -1.224489796 = 3.947278545 Simplifying x + -1.224489796 = 3.947278545 Reorder the terms: -1.224489796 + x = 3.947278545 Solving -1.224489796 + x = 3.947278545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = 3.947278545 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 3.947278545 + 1.224489796 x = 3.947278545 + 1.224489796 Combine like terms: 3.947278545 + 1.224489796 = 5.171768341 x = 5.171768341 Simplifying x = 5.171768341

Subproblem 2

x + -1.224489796 = -3.947278545 Simplifying x + -1.224489796 = -3.947278545 Reorder the terms: -1.224489796 + x = -3.947278545 Solving -1.224489796 + x = -3.947278545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = -3.947278545 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -3.947278545 + 1.224489796 x = -3.947278545 + 1.224489796 Combine like terms: -3.947278545 + 1.224489796 = -2.722788749 x = -2.722788749 Simplifying x = -2.722788749

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.171768341, -2.722788749}

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