20=4.9x^2+15x

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Solution for 20=4.9x^2+15x equation:


Simplifying
20 = 4.9x2 + 15x

Reorder the terms:
20 = 15x + 4.9x2

Solving
20 = 15x + 4.9x2

Solving for variable 'x'.

Reorder the terms:
20 + -15x + -4.9x2 = 15x + -15x + 4.9x2 + -4.9x2

Combine like terms: 15x + -15x = 0
20 + -15x + -4.9x2 = 0 + 4.9x2 + -4.9x2
20 + -15x + -4.9x2 = 4.9x2 + -4.9x2

Combine like terms: 4.9x2 + -4.9x2 = 0.0
20 + -15x + -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'.
-4.081632653 + 3.06122449x + x2 = 0

Move the constant term to the right:

Add '4.081632653' to each side of the equation.
-4.081632653 + 3.06122449x + 4.081632653 + x2 = 0 + 4.081632653

Reorder the terms:
-4.081632653 + 4.081632653 + 3.06122449x + x2 = 0 + 4.081632653

Combine like terms: -4.081632653 + 4.081632653 = 0.000000000
0.000000000 + 3.06122449x + x2 = 0 + 4.081632653
3.06122449x + x2 = 0 + 4.081632653

Combine like terms: 0 + 4.081632653 = 4.081632653
3.06122449x + x2 = 4.081632653

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 = 4.081632653 + 2.342773845

Reorder the terms:
2.342773845 + 3.06122449x + x2 = 4.081632653 + 2.342773845

Combine like terms: 4.081632653 + 2.342773845 = 6.424406498
2.342773845 + 3.06122449x + x2 = 6.424406498

Factor a perfect square on the left side:
(x + 1.530612245)(x + 1.530612245) = 6.424406498

Calculate the square root of the right side: 2.534641296

Break this problem into two subproblems by setting 
(x + 1.530612245) equal to 2.534641296 and -2.534641296.

Subproblem 1

x + 1.530612245 = 2.534641296 Simplifying x + 1.530612245 = 2.534641296 Reorder the terms: 1.530612245 + x = 2.534641296 Solving 1.530612245 + x = 2.534641296 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 = 2.534641296 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = 2.534641296 + -1.530612245 x = 2.534641296 + -1.530612245 Combine like terms: 2.534641296 + -1.530612245 = 1.004029051 x = 1.004029051 Simplifying x = 1.004029051

Subproblem 2

x + 1.530612245 = -2.534641296 Simplifying x + 1.530612245 = -2.534641296 Reorder the terms: 1.530612245 + x = -2.534641296 Solving 1.530612245 + x = -2.534641296 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 = -2.534641296 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = -2.534641296 + -1.530612245 x = -2.534641296 + -1.530612245 Combine like terms: -2.534641296 + -1.530612245 = -4.065253541 x = -4.065253541 Simplifying x = -4.065253541

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.004029051, -4.065253541}

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