4.9x^2+15x-69=0

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Solution for 4.9x^2+15x-69=0 equation: 


Simplifying
4.9x2 + 15x + -69 = 0

Reorder the terms:
-69 + 15x + 4.9x2 = 0

Solving
-69 + 15x + 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'.
-14.08163265 + 3.06122449x + x2 = 0

Move the constant term to the right:

Add '14.08163265' to each side of the equation.
-14.08163265 + 3.06122449x + 14.08163265 + x2 = 0 + 14.08163265

Reorder the terms:
-14.08163265 + 14.08163265 + 3.06122449x + x2 = 0 + 14.08163265

Combine like terms: -14.08163265 + 14.08163265 = 0.00000000
0.00000000 + 3.06122449x + x2 = 0 + 14.08163265
3.06122449x + x2 = 0 + 14.08163265

Combine like terms: 0 + 14.08163265 = 14.08163265
3.06122449x + x2 = 14.08163265

The x term is 3.06122449x.  Take half its coefficient (1.530612245).
Square it (2.342773845) and add it to both sides.

Add '2.342773845' to each side of the equation.
3.06122449x + 2.342773845 + x2 = 14.08163265 + 2.342773845

Reorder the terms:
2.342773845 + 3.06122449x + x2 = 14.08163265 + 2.342773845

Combine like terms: 14.08163265 + 2.342773845 = 16.424406495
2.342773845 + 3.06122449x + x2 = 16.424406495

Factor a perfect square on the left side:
(x + 1.530612245)(x + 1.530612245) = 16.424406495

Calculate the square root of the right side: 4.052703603

Break this problem into two subproblems by setting 
(x + 1.530612245) equal to 4.052703603 and -4.052703603.


Subproblem 1
x + 1.530612245 = 4.052703603

Simplifying
x + 1.530612245 = 4.052703603

Reorder the terms:
1.530612245 + x = 4.052703603

Solving
1.530612245 + x = 4.052703603

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.530612245' to each side of the equation.
1.530612245 + -1.530612245 + x = 4.052703603 + -1.530612245

Combine like terms: 1.530612245 + -1.530612245 = 0.000000000
0.000000000 + x = 4.052703603 + -1.530612245
x = 4.052703603 + -1.530612245

Combine like terms: 4.052703603 + -1.530612245 = 2.522091358
x = 2.522091358

Simplifying
x = 2.522091358


Subproblem 2
x + 1.530612245 = -4.052703603

Simplifying
x + 1.530612245 = -4.052703603

Reorder the terms:
1.530612245 + x = -4.052703603

Solving
1.530612245 + x = -4.052703603

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.530612245' to each side of the equation.
1.530612245 + -1.530612245 + x = -4.052703603 + -1.530612245

Combine like terms: 1.530612245 + -1.530612245 = 0.000000000
0.000000000 + x = -4.052703603 + -1.530612245
x = -4.052703603 + -1.530612245

Combine like terms: -4.052703603 + -1.530612245 = -5.583315848
x = -5.583315848

Simplifying
x = -5.583315848


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.522091358, -5.583315848}

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