(6x^2-3x+25)+(2x^2+5x-54)=

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Solution for (6x^2-3x+25)+(2x^2+5x-54)= equation:


Simplifying
(6x2 + -3x + 25) + (2x2 + 5x + -54) = 0

Reorder the terms:
(25 + -3x + 6x2) + (2x2 + 5x + -54) = 0

Remove parenthesis around (25 + -3x + 6x2)
25 + -3x + 6x2 + (2x2 + 5x + -54) = 0

Reorder the terms:
25 + -3x + 6x2 + (-54 + 5x + 2x2) = 0

Remove parenthesis around (-54 + 5x + 2x2)
25 + -3x + 6x2 + -54 + 5x + 2x2 = 0

Reorder the terms:
25 + -54 + -3x + 5x + 6x2 + 2x2 = 0

Combine like terms: 25 + -54 = -29
-29 + -3x + 5x + 6x2 + 2x2 = 0

Combine like terms: -3x + 5x = 2x
-29 + 2x + 6x2 + 2x2 = 0

Combine like terms: 6x2 + 2x2 = 8x2
-29 + 2x + 8x2 = 0

Solving
-29 + 2x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-3.625 + 0.25x + x2 = 0

Move the constant term to the right:

Add '3.625' to each side of the equation.
-3.625 + 0.25x + 3.625 + x2 = 0 + 3.625

Reorder the terms:
-3.625 + 3.625 + 0.25x + x2 = 0 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + 0.25x + x2 = 0 + 3.625
0.25x + x2 = 0 + 3.625

Combine like terms: 0 + 3.625 = 3.625
0.25x + x2 = 3.625

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 = 3.625 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 3.625 + 0.015625

Combine like terms: 3.625 + 0.015625 = 3.640625
0.015625 + 0.25x + x2 = 3.640625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 3.640625

Calculate the square root of the right side: 1.90804219

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.90804219 and -1.90804219.

Subproblem 1

x + 0.125 = 1.90804219 Simplifying x + 0.125 = 1.90804219 Reorder the terms: 0.125 + x = 1.90804219 Solving 0.125 + x = 1.90804219 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 = 1.90804219 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.90804219 + -0.125 x = 1.90804219 + -0.125 Combine like terms: 1.90804219 + -0.125 = 1.78304219 x = 1.78304219 Simplifying x = 1.78304219

Subproblem 2

x + 0.125 = -1.90804219 Simplifying x + 0.125 = -1.90804219 Reorder the terms: 0.125 + x = -1.90804219 Solving 0.125 + x = -1.90804219 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 = -1.90804219 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.90804219 + -0.125 x = -1.90804219 + -0.125 Combine like terms: -1.90804219 + -0.125 = -2.03304219 x = -2.03304219 Simplifying x = -2.03304219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.78304219, -2.03304219}

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