-1.80=4.9x-4.9(x^2)

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Solution for -1.80=4.9x-4.9(x^2) equation:


Simplifying
-1.80 = 4.9x + -4.9(x2)

Solving
-1.80 = 4.9x + -4.9x2

Solving for variable 'x'.

Reorder the terms:
-1.80 + -4.9x + 4.9x2 = 4.9x + -4.9x + -4.9x2 + 4.9x2

Combine like terms: 4.9x + -4.9x = 0.0
-1.80 + -4.9x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2
-1.80 + -4.9x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-1.80 + -4.9x + 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'.
-0.3673469388 + -1x + x2 = 0

Move the constant term to the right:

Add '0.3673469388' to each side of the equation.
-0.3673469388 + -1x + 0.3673469388 + x2 = 0 + 0.3673469388

Reorder the terms:
-0.3673469388 + 0.3673469388 + -1x + x2 = 0 + 0.3673469388

Combine like terms: -0.3673469388 + 0.3673469388 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + 0.3673469388
-1x + x2 = 0 + 0.3673469388

Combine like terms: 0 + 0.3673469388 = 0.3673469388
-1x + x2 = 0.3673469388

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.3673469388 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.3673469388 + 0.25

Combine like terms: 0.3673469388 + 0.25 = 0.6173469388
0.25 + -1x + x2 = 0.6173469388

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.6173469388

Calculate the square root of the right side: 0.785714286

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.785714286 and -0.785714286.

Subproblem 1

x + -0.5 = 0.785714286 Simplifying x + -0.5 = 0.785714286 Reorder the terms: -0.5 + x = 0.785714286 Solving -0.5 + x = 0.785714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.785714286 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.785714286 + 0.5 x = 0.785714286 + 0.5 Combine like terms: 0.785714286 + 0.5 = 1.285714286 x = 1.285714286 Simplifying x = 1.285714286

Subproblem 2

x + -0.5 = -0.785714286 Simplifying x + -0.5 = -0.785714286 Reorder the terms: -0.5 + x = -0.785714286 Solving -0.5 + x = -0.785714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.785714286 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.785714286 + 0.5 x = -0.785714286 + 0.5 Combine like terms: -0.785714286 + 0.5 = -0.285714286 x = -0.285714286 Simplifying x = -0.285714286

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.285714286, -0.285714286}

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