4x^2+9x=105

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Solution for 4x^2+9x=105 equation:


Simplifying
4x2 + 9x = 105

Reorder the terms:
9x + 4x2 = 105

Solving
9x + 4x2 = 105

Solving for variable 'x'.

Reorder the terms:
-105 + 9x + 4x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + 9x + 4x2 = 0

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

Divide each side by '4'.
-26.25 + 2.25x + x2 = 0

Move the constant term to the right:

Add '26.25' to each side of the equation.
-26.25 + 2.25x + 26.25 + x2 = 0 + 26.25

Reorder the terms:
-26.25 + 26.25 + 2.25x + x2 = 0 + 26.25

Combine like terms: -26.25 + 26.25 = 0.00
0.00 + 2.25x + x2 = 0 + 26.25
2.25x + x2 = 0 + 26.25

Combine like terms: 0 + 26.25 = 26.25
2.25x + x2 = 26.25

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 = 26.25 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 26.25 + 1.265625

Combine like terms: 26.25 + 1.265625 = 27.515625
1.265625 + 2.25x + x2 = 27.515625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 27.515625

Calculate the square root of the right side: 5.245533815

Break this problem into two subproblems by setting 
(x + 1.125) equal to 5.245533815 and -5.245533815.

Subproblem 1

x + 1.125 = 5.245533815 Simplifying x + 1.125 = 5.245533815 Reorder the terms: 1.125 + x = 5.245533815 Solving 1.125 + x = 5.245533815 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 = 5.245533815 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 5.245533815 + -1.125 x = 5.245533815 + -1.125 Combine like terms: 5.245533815 + -1.125 = 4.120533815 x = 4.120533815 Simplifying x = 4.120533815

Subproblem 2

x + 1.125 = -5.245533815 Simplifying x + 1.125 = -5.245533815 Reorder the terms: 1.125 + x = -5.245533815 Solving 1.125 + x = -5.245533815 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 = -5.245533815 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -5.245533815 + -1.125 x = -5.245533815 + -1.125 Combine like terms: -5.245533815 + -1.125 = -6.370533815 x = -6.370533815 Simplifying x = -6.370533815

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.120533815, -6.370533815}

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