5x^2+10x=9

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Solution for 5x^2+10x=9 equation:


Simplifying
5x2 + 10x = 9

Reorder the terms:
10x + 5x2 = 9

Solving
10x + 5x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 10x + 5x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 10x + 5x2 = 0

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

Divide each side by '5'.
-1.8 + 2x + x2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 2x + 1.8 + x2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 2x + x2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 2x + x2 = 0 + 1.8
2x + x2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
2x + x2 = 1.8

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.8 + 1

Reorder the terms:
1 + 2x + x2 = 1.8 + 1

Combine like terms: 1.8 + 1 = 2.8
1 + 2x + x2 = 2.8

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.8

Calculate the square root of the right side: 1.673320053

Break this problem into two subproblems by setting 
(x + 1) equal to 1.673320053 and -1.673320053.

Subproblem 1

x + 1 = 1.673320053 Simplifying x + 1 = 1.673320053 Reorder the terms: 1 + x = 1.673320053 Solving 1 + x = 1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.673320053 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.673320053 + -1 x = 1.673320053 + -1 Combine like terms: 1.673320053 + -1 = 0.673320053 x = 0.673320053 Simplifying x = 0.673320053

Subproblem 2

x + 1 = -1.673320053 Simplifying x + 1 = -1.673320053 Reorder the terms: 1 + x = -1.673320053 Solving 1 + x = -1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.673320053 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.673320053 + -1 x = -1.673320053 + -1 Combine like terms: -1.673320053 + -1 = -2.673320053 x = -2.673320053 Simplifying x = -2.673320053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.673320053, -2.673320053}

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