5x^2+9x=7

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Solution for 5x^2+9x=7 equation:


Simplifying
5x2 + 9x = 7

Reorder the terms:
9x + 5x2 = 7

Solving
9x + 5x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 9x + 5x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 9x + 5x2 = 0

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

Divide each side by '5'.
-1.4 + 1.8x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 1.8x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 1.8x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 1.8x + x2 = 0 + 1.4
1.8x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
1.8x + x2 = 1.4

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 1.4 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 1.4 + 0.81

Combine like terms: 1.4 + 0.81 = 2.21
0.81 + 1.8x + x2 = 2.21

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 2.21

Calculate the square root of the right side: 1.486606875

Break this problem into two subproblems by setting 
(x + 0.9) equal to 1.486606875 and -1.486606875.

Subproblem 1

x + 0.9 = 1.486606875 Simplifying x + 0.9 = 1.486606875 Reorder the terms: 0.9 + x = 1.486606875 Solving 0.9 + x = 1.486606875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.486606875 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.486606875 + -0.9 x = 1.486606875 + -0.9 Combine like terms: 1.486606875 + -0.9 = 0.586606875 x = 0.586606875 Simplifying x = 0.586606875

Subproblem 2

x + 0.9 = -1.486606875 Simplifying x + 0.9 = -1.486606875 Reorder the terms: 0.9 + x = -1.486606875 Solving 0.9 + x = -1.486606875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.486606875 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.486606875 + -0.9 x = -1.486606875 + -0.9 Combine like terms: -1.486606875 + -0.9 = -2.386606875 x = -2.386606875 Simplifying x = -2.386606875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.586606875, -2.386606875}

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