10x^2+4x+5x=3

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Solution for 10x^2+4x+5x=3 equation:


Simplifying
10x2 + 4x + 5x = 3

Reorder the terms:
4x + 5x + 10x2 = 3

Combine like terms: 4x + 5x = 9x
9x + 10x2 = 3

Solving
9x + 10x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 9x + 10x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 9x + 10x2 = 0

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

Divide each side by '10'.
-0.3 + 0.9x + x2 = 0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 0.9x + 0.3 + x2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 0.9x + x2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 0.9x + x2 = 0 + 0.3
0.9x + x2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
0.9x + x2 = 0.3

The x term is 0.9x.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x + 0.2025 + x2 = 0.3 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = 0.3 + 0.2025

Combine like terms: 0.3 + 0.2025 = 0.5025
0.2025 + 0.9x + x2 = 0.5025

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = 0.5025

Calculate the square root of the right side: 0.708872344

Break this problem into two subproblems by setting 
(x + 0.45) equal to 0.708872344 and -0.708872344.

Subproblem 1

x + 0.45 = 0.708872344 Simplifying x + 0.45 = 0.708872344 Reorder the terms: 0.45 + x = 0.708872344 Solving 0.45 + x = 0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 0.708872344 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 0.708872344 + -0.45 x = 0.708872344 + -0.45 Combine like terms: 0.708872344 + -0.45 = 0.258872344 x = 0.258872344 Simplifying x = 0.258872344

Subproblem 2

x + 0.45 = -0.708872344 Simplifying x + 0.45 = -0.708872344 Reorder the terms: 0.45 + x = -0.708872344 Solving 0.45 + x = -0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -0.708872344 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -0.708872344 + -0.45 x = -0.708872344 + -0.45 Combine like terms: -0.708872344 + -0.45 = -1.158872344 x = -1.158872344 Simplifying x = -1.158872344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.258872344, -1.158872344}

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