(4x^2-4x+16)+(5x^2+9x-72)=

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Solution for (4x^2-4x+16)+(5x^2+9x-72)= equation:


Simplifying
(4x2 + -4x + 16) + (5x2 + 9x + -72) = 0

Reorder the terms:
(16 + -4x + 4x2) + (5x2 + 9x + -72) = 0

Remove parenthesis around (16 + -4x + 4x2)
16 + -4x + 4x2 + (5x2 + 9x + -72) = 0

Reorder the terms:
16 + -4x + 4x2 + (-72 + 9x + 5x2) = 0

Remove parenthesis around (-72 + 9x + 5x2)
16 + -4x + 4x2 + -72 + 9x + 5x2 = 0

Reorder the terms:
16 + -72 + -4x + 9x + 4x2 + 5x2 = 0

Combine like terms: 16 + -72 = -56
-56 + -4x + 9x + 4x2 + 5x2 = 0

Combine like terms: -4x + 9x = 5x
-56 + 5x + 4x2 + 5x2 = 0

Combine like terms: 4x2 + 5x2 = 9x2
-56 + 5x + 9x2 = 0

Solving
-56 + 5x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-6.222222222 + 0.5555555556x + x2 = 0

Move the constant term to the right:

Add '6.222222222' to each side of the equation.
-6.222222222 + 0.5555555556x + 6.222222222 + x2 = 0 + 6.222222222

Reorder the terms:
-6.222222222 + 6.222222222 + 0.5555555556x + x2 = 0 + 6.222222222

Combine like terms: -6.222222222 + 6.222222222 = 0.000000000
0.000000000 + 0.5555555556x + x2 = 0 + 6.222222222
0.5555555556x + x2 = 0 + 6.222222222

Combine like terms: 0 + 6.222222222 = 6.222222222
0.5555555556x + x2 = 6.222222222

The x term is 0.5555555556x.  Take half its coefficient (0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
0.5555555556x + 0.07716049384 + x2 = 6.222222222 + 0.07716049384

Reorder the terms:
0.07716049384 + 0.5555555556x + x2 = 6.222222222 + 0.07716049384

Combine like terms: 6.222222222 + 0.07716049384 = 6.29938271584
0.07716049384 + 0.5555555556x + x2 = 6.29938271584

Factor a perfect square on the left side:
(x + 0.2777777778)(x + 0.2777777778) = 6.29938271584

Calculate the square root of the right side: 2.509857111

Break this problem into two subproblems by setting 
(x + 0.2777777778) equal to 2.509857111 and -2.509857111.

Subproblem 1

x + 0.2777777778 = 2.509857111 Simplifying x + 0.2777777778 = 2.509857111 Reorder the terms: 0.2777777778 + x = 2.509857111 Solving 0.2777777778 + x = 2.509857111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 2.509857111 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 2.509857111 + -0.2777777778 x = 2.509857111 + -0.2777777778 Combine like terms: 2.509857111 + -0.2777777778 = 2.2320793332 x = 2.2320793332 Simplifying x = 2.2320793332

Subproblem 2

x + 0.2777777778 = -2.509857111 Simplifying x + 0.2777777778 = -2.509857111 Reorder the terms: 0.2777777778 + x = -2.509857111 Solving 0.2777777778 + x = -2.509857111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -2.509857111 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -2.509857111 + -0.2777777778 x = -2.509857111 + -0.2777777778 Combine like terms: -2.509857111 + -0.2777777778 = -2.7876348888 x = -2.7876348888 Simplifying x = -2.7876348888

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.2320793332, -2.7876348888}

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