2-x^2=9.8x

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Solution for 2-x^2=9.8x equation:


Simplifying
2 + -1x2 = 9.8x

Solving
2 + -1x2 = 9.8x

Solving for variable 'x'.

Reorder the terms:
2 + -9.8x + -1x2 = 9.8x + -9.8x

Combine like terms: 9.8x + -9.8x = 0.0
2 + -9.8x + -1x2 = 0.0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + 9.8x + x2 = 0.0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 9.8x + 2 + x2 = 0.0 + 2

Reorder the terms:
-2 + 2 + 9.8x + x2 = 0.0 + 2

Combine like terms: -2 + 2 = 0
0 + 9.8x + x2 = 0.0 + 2
9.8x + x2 = 0.0 + 2

Combine like terms: 0.0 + 2 = 2
9.8x + x2 = 2

The x term is 9.8x.  Take half its coefficient (4.9).
Square it (24.01) and add it to both sides.

Add '24.01' to each side of the equation.
9.8x + 24.01 + x2 = 2 + 24.01

Reorder the terms:
24.01 + 9.8x + x2 = 2 + 24.01

Combine like terms: 2 + 24.01 = 26.01
24.01 + 9.8x + x2 = 26.01

Factor a perfect square on the left side:
(x + 4.9)(x + 4.9) = 26.01

Calculate the square root of the right side: 5.1

Break this problem into two subproblems by setting 
(x + 4.9) equal to 5.1 and -5.1.

Subproblem 1

x + 4.9 = 5.1 Simplifying x + 4.9 = 5.1 Reorder the terms: 4.9 + x = 5.1 Solving 4.9 + x = 5.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.9' to each side of the equation. 4.9 + -4.9 + x = 5.1 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + x = 5.1 + -4.9 x = 5.1 + -4.9 Combine like terms: 5.1 + -4.9 = 0.2 x = 0.2 Simplifying x = 0.2

Subproblem 2

x + 4.9 = -5.1 Simplifying x + 4.9 = -5.1 Reorder the terms: 4.9 + x = -5.1 Solving 4.9 + x = -5.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.9' to each side of the equation. 4.9 + -4.9 + x = -5.1 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + x = -5.1 + -4.9 x = -5.1 + -4.9 Combine like terms: -5.1 + -4.9 = -10 x = -10 Simplifying x = -10

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2, -10}

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