0=(-4.9)x^2+40x+15

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Solution for 0=(-4.9)x^2+40x+15 equation:


Simplifying
0 = (-4.9) * x2 + 40x + 15

Reorder the terms:
0 = 15 + 40x + -4.9x2

Solving
0 = 15 + 40x + -4.9x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + -40x + 4.9x2 = 15 + 40x + -4.9x2 + -15 + -40x + 4.9x2

Reorder the terms:
-15 + -40x + 4.9x2 = 15 + -15 + 40x + -40x + -4.9x2 + 4.9x2

Combine like terms: 15 + -15 = 0
-15 + -40x + 4.9x2 = 0 + 40x + -40x + -4.9x2 + 4.9x2
-15 + -40x + 4.9x2 = 40x + -40x + -4.9x2 + 4.9x2

Combine like terms: 40x + -40x = 0
-15 + -40x + 4.9x2 = 0 + -4.9x2 + 4.9x2
-15 + -40x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-15 + -40x + 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'.
-3.06122449 + -8.163265306x + x2 = 0

Move the constant term to the right:

Add '3.06122449' to each side of the equation.
-3.06122449 + -8.163265306x + 3.06122449 + x2 = 0 + 3.06122449

Reorder the terms:
-3.06122449 + 3.06122449 + -8.163265306x + x2 = 0 + 3.06122449

Combine like terms: -3.06122449 + 3.06122449 = 0.00000000
0.00000000 + -8.163265306x + x2 = 0 + 3.06122449
-8.163265306x + x2 = 0 + 3.06122449

Combine like terms: 0 + 3.06122449 = 3.06122449
-8.163265306x + x2 = 3.06122449

The x term is -8.163265306x.  Take half its coefficient (-4.081632653).
Square it (16.65972511) and add it to both sides.

Add '16.65972511' to each side of the equation.
-8.163265306x + 16.65972511 + x2 = 3.06122449 + 16.65972511

Reorder the terms:
16.65972511 + -8.163265306x + x2 = 3.06122449 + 16.65972511

Combine like terms: 3.06122449 + 16.65972511 = 19.7209496
16.65972511 + -8.163265306x + x2 = 19.7209496

Factor a perfect square on the left side:
(x + -4.081632653)(x + -4.081632653) = 19.7209496

Calculate the square root of the right side: 4.440827581

Break this problem into two subproblems by setting 
(x + -4.081632653) equal to 4.440827581 and -4.440827581.

Subproblem 1

x + -4.081632653 = 4.440827581 Simplifying x + -4.081632653 = 4.440827581 Reorder the terms: -4.081632653 + x = 4.440827581 Solving -4.081632653 + x = 4.440827581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + x = 4.440827581 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + x = 4.440827581 + 4.081632653 x = 4.440827581 + 4.081632653 Combine like terms: 4.440827581 + 4.081632653 = 8.522460234 x = 8.522460234 Simplifying x = 8.522460234

Subproblem 2

x + -4.081632653 = -4.440827581 Simplifying x + -4.081632653 = -4.440827581 Reorder the terms: -4.081632653 + x = -4.440827581 Solving -4.081632653 + x = -4.440827581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + x = -4.440827581 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + x = -4.440827581 + 4.081632653 x = -4.440827581 + 4.081632653 Combine like terms: -4.440827581 + 4.081632653 = -0.359194928 x = -0.359194928 Simplifying x = -0.359194928

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.522460234, -0.359194928}

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