10x^2+2x=9

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Solution for 10x^2+2x=9 equation:


Simplifying
10x2 + 2x = 9

Reorder the terms:
2x + 10x2 = 9

Solving
2x + 10x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 2x + 10x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 2x + 10x2 = 0

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

Divide each side by '10'.
-0.9 + 0.2x + x2 = 0

Move the constant term to the right:

Add '0.9' to each side of the equation.
-0.9 + 0.2x + 0.9 + x2 = 0 + 0.9

Reorder the terms:
-0.9 + 0.9 + 0.2x + x2 = 0 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + 0.2x + x2 = 0 + 0.9
0.2x + x2 = 0 + 0.9

Combine like terms: 0 + 0.9 = 0.9
0.2x + x2 = 0.9

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 0.9 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 0.9 + 0.01

Combine like terms: 0.9 + 0.01 = 0.91
0.01 + 0.2x + x2 = 0.91

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 0.91

Calculate the square root of the right side: 0.953939201

Break this problem into two subproblems by setting 
(x + 0.1) equal to 0.953939201 and -0.953939201.

Subproblem 1

x + 0.1 = 0.953939201 Simplifying x + 0.1 = 0.953939201 Reorder the terms: 0.1 + x = 0.953939201 Solving 0.1 + x = 0.953939201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.953939201 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.953939201 + -0.1 x = 0.953939201 + -0.1 Combine like terms: 0.953939201 + -0.1 = 0.853939201 x = 0.853939201 Simplifying x = 0.853939201

Subproblem 2

x + 0.1 = -0.953939201 Simplifying x + 0.1 = -0.953939201 Reorder the terms: 0.1 + x = -0.953939201 Solving 0.1 + x = -0.953939201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.953939201 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.953939201 + -0.1 x = -0.953939201 + -0.1 Combine like terms: -0.953939201 + -0.1 = -1.053939201 x = -1.053939201 Simplifying x = -1.053939201

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.853939201, -1.053939201}

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