4x^2+9x=4

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


Simplifying
4x2 + 9x = 4

Reorder the terms:
9x + 4x2 = 4

Solving
9x + 4x2 = 4

Solving for variable 'x'.

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

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

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

Divide each side by '4'.
-1 + 2.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.25x + x2 = 0 + 1
2.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.25x + x2 = 1

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 = 1 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 1 + 1.265625

Combine like terms: 1 + 1.265625 = 2.265625
1.265625 + 2.25x + x2 = 2.265625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.505199322 and -1.505199322.

Subproblem 1

x + 1.125 = 1.505199322 Simplifying x + 1.125 = 1.505199322 Reorder the terms: 1.125 + x = 1.505199322 Solving 1.125 + x = 1.505199322 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 = 1.505199322 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.505199322 + -1.125 x = 1.505199322 + -1.125 Combine like terms: 1.505199322 + -1.125 = 0.380199322 x = 0.380199322 Simplifying x = 0.380199322

Subproblem 2

x + 1.125 = -1.505199322 Simplifying x + 1.125 = -1.505199322 Reorder the terms: 1.125 + x = -1.505199322 Solving 1.125 + x = -1.505199322 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 = -1.505199322 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.505199322 + -1.125 x = -1.505199322 + -1.125 Combine like terms: -1.505199322 + -1.125 = -2.630199322 x = -2.630199322 Simplifying x = -2.630199322

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.380199322, -2.630199322}

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