4x^2+4x-9=5x+3

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Solution for 4x^2+4x-9=5x+3 equation:


Simplifying
4x2 + 4x + -9 = 5x + 3

Reorder the terms:
-9 + 4x + 4x2 = 5x + 3

Reorder the terms:
-9 + 4x + 4x2 = 3 + 5x

Solving
-9 + 4x + 4x2 = 3 + 5x

Solving for variable 'x'.

Reorder the terms:
-9 + -3 + 4x + -5x + 4x2 = 3 + 5x + -3 + -5x

Combine like terms: -9 + -3 = -12
-12 + 4x + -5x + 4x2 = 3 + 5x + -3 + -5x

Combine like terms: 4x + -5x = -1x
-12 + -1x + 4x2 = 3 + 5x + -3 + -5x

Reorder the terms:
-12 + -1x + 4x2 = 3 + -3 + 5x + -5x

Combine like terms: 3 + -3 = 0
-12 + -1x + 4x2 = 0 + 5x + -5x
-12 + -1x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-12 + -1x + 4x2 = 0

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

Divide each side by '4'.
-3 + -0.25x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -0.25x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -0.25x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -0.25x + x2 = 0 + 3
-0.25x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-0.25x + x2 = 3

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 3 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 3 + 0.015625

Combine like terms: 3 + 0.015625 = 3.015625
0.015625 + -0.25x + x2 = 3.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 3.015625

Calculate the square root of the right side: 1.736555499

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.736555499 and -1.736555499.

Subproblem 1

x + -0.125 = 1.736555499 Simplifying x + -0.125 = 1.736555499 Reorder the terms: -0.125 + x = 1.736555499 Solving -0.125 + x = 1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.736555499 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.736555499 + 0.125 x = 1.736555499 + 0.125 Combine like terms: 1.736555499 + 0.125 = 1.861555499 x = 1.861555499 Simplifying x = 1.861555499

Subproblem 2

x + -0.125 = -1.736555499 Simplifying x + -0.125 = -1.736555499 Reorder the terms: -0.125 + x = -1.736555499 Solving -0.125 + x = -1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.736555499 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.736555499 + 0.125 x = -1.736555499 + 0.125 Combine like terms: -1.736555499 + 0.125 = -1.611555499 x = -1.611555499 Simplifying x = -1.611555499

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.861555499, -1.611555499}

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