0.565145x^2+4.49x-100=0

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Solution for 0.565145x^2+4.49x-100=0 equation:


Simplifying
0.565145x2 + 4.49x + -100 = 0

Reorder the terms:
-100 + 4.49x + 0.565145x2 = 0

Solving
-100 + 4.49x + 0.565145x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.565145 the coefficient of the squared term: 

Divide each side by '0.565145'.
-176.9457396 + 7.944863708x + x2 = 0

Move the constant term to the right:

Add '176.9457396' to each side of the equation.
-176.9457396 + 7.944863708x + 176.9457396 + x2 = 0 + 176.9457396

Reorder the terms:
-176.9457396 + 176.9457396 + 7.944863708x + x2 = 0 + 176.9457396

Combine like terms: -176.9457396 + 176.9457396 = 0.0000000
0.0000000 + 7.944863708x + x2 = 0 + 176.9457396
7.944863708x + x2 = 0 + 176.9457396

Combine like terms: 0 + 176.9457396 = 176.9457396
7.944863708x + x2 = 176.9457396

The x term is 7.944863708x.  Take half its coefficient (3.972431854).
Square it (15.78021483) and add it to both sides.

Add '15.78021483' to each side of the equation.
7.944863708x + 15.78021483 + x2 = 176.9457396 + 15.78021483

Reorder the terms:
15.78021483 + 7.944863708x + x2 = 176.9457396 + 15.78021483

Combine like terms: 176.9457396 + 15.78021483 = 192.72595443
15.78021483 + 7.944863708x + x2 = 192.72595443

Factor a perfect square on the left side:
(x + 3.972431854)(x + 3.972431854) = 192.72595443

Calculate the square root of the right side: 13.88257737

Break this problem into two subproblems by setting 
(x + 3.972431854) equal to 13.88257737 and -13.88257737.

Subproblem 1

x + 3.972431854 = 13.88257737 Simplifying x + 3.972431854 = 13.88257737 Reorder the terms: 3.972431854 + x = 13.88257737 Solving 3.972431854 + x = 13.88257737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.972431854' to each side of the equation. 3.972431854 + -3.972431854 + x = 13.88257737 + -3.972431854 Combine like terms: 3.972431854 + -3.972431854 = 0.000000000 0.000000000 + x = 13.88257737 + -3.972431854 x = 13.88257737 + -3.972431854 Combine like terms: 13.88257737 + -3.972431854 = 9.910145516 x = 9.910145516 Simplifying x = 9.910145516

Subproblem 2

x + 3.972431854 = -13.88257737 Simplifying x + 3.972431854 = -13.88257737 Reorder the terms: 3.972431854 + x = -13.88257737 Solving 3.972431854 + x = -13.88257737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.972431854' to each side of the equation. 3.972431854 + -3.972431854 + x = -13.88257737 + -3.972431854 Combine like terms: 3.972431854 + -3.972431854 = 0.000000000 0.000000000 + x = -13.88257737 + -3.972431854 x = -13.88257737 + -3.972431854 Combine like terms: -13.88257737 + -3.972431854 = -17.855009224 x = -17.855009224 Simplifying x = -17.855009224

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.910145516, -17.855009224}

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