-42=2.8x+.5(-9.8)x^2

Solution for -42=2.8x+.5(-9.8)x^2 equation:

Simplifying
-42 = 2.8x + 0.5(-9.8) * x2

Multiply 0.5 * -9.8
-42 = 2.8x + -4.9x2

Solving
-42 = 2.8x + -4.9x2

Solving for variable 'x'.

Reorder the terms:
-42 + -2.8x + 4.9x2 = 2.8x + -2.8x + -4.9x2 + 4.9x2

Combine like terms: 2.8x + -2.8x = 0.0
-42 + -2.8x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2
-42 + -2.8x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-42 + -2.8x + 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'.
-8.571428571 + -0.5714285714x + x2 = 0

Move the constant term to the right:

Add '8.571428571' to each side of the equation.
-8.571428571 + -0.5714285714x + 8.571428571 + x2 = 0 + 8.571428571

Reorder the terms:
-8.571428571 + 8.571428571 + -0.5714285714x + x2 = 0 + 8.571428571

Combine like terms: -8.571428571 + 8.571428571 = 0.000000000
0.000000000 + -0.5714285714x + x2 = 0 + 8.571428571
-0.5714285714x + x2 = 0 + 8.571428571

Combine like terms: 0 + 8.571428571 = 8.571428571
-0.5714285714x + x2 = 8.571428571

The x term is -0.5714285714x.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714x + 0.08163265305 + x2 = 8.571428571 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714x + x2 = 8.571428571 + 0.08163265305

Combine like terms: 8.571428571 + 0.08163265305 = 8.65306122405
0.08163265305 + -0.5714285714x + x2 = 8.65306122405

Factor a perfect square on the left side:
(x + -0.2857142857)(x + -0.2857142857) = 8.65306122405

Calculate the square root of the right side: 2.941608612

Break this problem into two subproblems by setting 
(x + -0.2857142857) equal to 2.941608612 and -2.941608612.

Subproblem 1
x + -0.2857142857 = 2.941608612

Simplifying
x + -0.2857142857 = 2.941608612

Reorder the terms:
-0.2857142857 + x = 2.941608612

Solving
-0.2857142857 + x = 2.941608612

Solving for variable 'x'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = 2.941608612 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = 2.941608612 + 0.2857142857
x = 2.941608612 + 0.2857142857

Combine like terms: 2.941608612 + 0.2857142857 = 3.2273228977
x = 3.2273228977

Simplifying
x = 3.2273228977

Subproblem 2
x + -0.2857142857 = -2.941608612

Simplifying
x + -0.2857142857 = -2.941608612

Reorder the terms:
-0.2857142857 + x = -2.941608612

Solving
-0.2857142857 + x = -2.941608612

Solving for variable 'x'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = -2.941608612 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = -2.941608612 + 0.2857142857
x = -2.941608612 + 0.2857142857

Combine like terms: -2.941608612 + 0.2857142857 = -2.6558943263
x = -2.6558943263

Simplifying
x = -2.6558943263

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.2273228977, -2.6558943263}