4x^2+9x=25

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Solution for 4x^2+9x=25 equation:


Simplifying
4x2 + 9x = 25

Reorder the terms:
9x + 4x2 = 25

Solving
9x + 4x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 9x + 4x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 9x + 4x2 = 0

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

Divide each side by '4'.
-6.25 + 2.25x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 2.25x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 2.25x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 2.25x + x2 = 0 + 6.25
2.25x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
2.25x + x2 = 6.25

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 6.25 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 6.25 + 1.265625

Combine like terms: 6.25 + 1.265625 = 7.515625
1.265625 + 2.25x + x2 = 7.515625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 7.515625

Calculate the square root of the right side: 2.741464025

Break this problem into two subproblems by setting 
(x + 1.125) equal to 2.741464025 and -2.741464025.

Subproblem 1

x + 1.125 = 2.741464025 Simplifying x + 1.125 = 2.741464025 Reorder the terms: 1.125 + x = 2.741464025 Solving 1.125 + x = 2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 2.741464025 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.741464025 + -1.125 x = 2.741464025 + -1.125 Combine like terms: 2.741464025 + -1.125 = 1.616464025 x = 1.616464025 Simplifying x = 1.616464025

Subproblem 2

x + 1.125 = -2.741464025 Simplifying x + 1.125 = -2.741464025 Reorder the terms: 1.125 + x = -2.741464025 Solving 1.125 + x = -2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -2.741464025 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.741464025 + -1.125 x = -2.741464025 + -1.125 Combine like terms: -2.741464025 + -1.125 = -3.866464025 x = -3.866464025 Simplifying x = -3.866464025

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.616464025, -3.866464025}

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