(2x^2-3x+24)+(2x^2+5x-55)=

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Solution for (2x^2-3x+24)+(2x^2+5x-55)= equation:


Simplifying
(2x2 + -3x + 24) + (2x2 + 5x + -55) = 0

Reorder the terms:
(24 + -3x + 2x2) + (2x2 + 5x + -55) = 0

Remove parenthesis around (24 + -3x + 2x2)
24 + -3x + 2x2 + (2x2 + 5x + -55) = 0

Reorder the terms:
24 + -3x + 2x2 + (-55 + 5x + 2x2) = 0

Remove parenthesis around (-55 + 5x + 2x2)
24 + -3x + 2x2 + -55 + 5x + 2x2 = 0

Reorder the terms:
24 + -55 + -3x + 5x + 2x2 + 2x2 = 0

Combine like terms: 24 + -55 = -31
-31 + -3x + 5x + 2x2 + 2x2 = 0

Combine like terms: -3x + 5x = 2x
-31 + 2x + 2x2 + 2x2 = 0

Combine like terms: 2x2 + 2x2 = 4x2
-31 + 2x + 4x2 = 0

Solving
-31 + 2x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-7.75 + 0.5x + x2 = 0

Move the constant term to the right:

Add '7.75' to each side of the equation.
-7.75 + 0.5x + 7.75 + x2 = 0 + 7.75

Reorder the terms:
-7.75 + 7.75 + 0.5x + x2 = 0 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + 0.5x + x2 = 0 + 7.75
0.5x + x2 = 0 + 7.75

Combine like terms: 0 + 7.75 = 7.75
0.5x + x2 = 7.75

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 7.75 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 7.75 + 0.0625

Combine like terms: 7.75 + 0.0625 = 7.8125
0.0625 + 0.5x + x2 = 7.8125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 7.8125

Calculate the square root of the right side: 2.795084972

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.795084972 and -2.795084972.

Subproblem 1

x + 0.25 = 2.795084972 Simplifying x + 0.25 = 2.795084972 Reorder the terms: 0.25 + x = 2.795084972 Solving 0.25 + x = 2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.795084972 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.795084972 + -0.25 x = 2.795084972 + -0.25 Combine like terms: 2.795084972 + -0.25 = 2.545084972 x = 2.545084972 Simplifying x = 2.545084972

Subproblem 2

x + 0.25 = -2.795084972 Simplifying x + 0.25 = -2.795084972 Reorder the terms: 0.25 + x = -2.795084972 Solving 0.25 + x = -2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.795084972 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.795084972 + -0.25 x = -2.795084972 + -0.25 Combine like terms: -2.795084972 + -0.25 = -3.045084972 x = -3.045084972 Simplifying x = -3.045084972

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.545084972, -3.045084972}

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