x^2+55x-66=78

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Solution for x^2+55x-66=78 equation:


Simplifying
x2 + 55x + -66 = 78

Reorder the terms:
-66 + 55x + x2 = 78

Solving
-66 + 55x + x2 = 78

Solving for variable 'x'.

Reorder the terms:
-66 + -78 + 55x + x2 = 78 + -78

Combine like terms: -66 + -78 = -144
-144 + 55x + x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-144 + 55x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 55x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 55x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 55x + x2 = 0 + 144
55x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
55x + x2 = 144

The x term is 55x.  Take half its coefficient (27.5).
Square it (756.25) and add it to both sides.

Add '756.25' to each side of the equation.
55x + 756.25 + x2 = 144 + 756.25

Reorder the terms:
756.25 + 55x + x2 = 144 + 756.25

Combine like terms: 144 + 756.25 = 900.25
756.25 + 55x + x2 = 900.25

Factor a perfect square on the left side:
(x + 27.5)(x + 27.5) = 900.25

Calculate the square root of the right side: 30.004166377

Break this problem into two subproblems by setting 
(x + 27.5) equal to 30.004166377 and -30.004166377.

Subproblem 1

x + 27.5 = 30.004166377 Simplifying x + 27.5 = 30.004166377 Reorder the terms: 27.5 + x = 30.004166377 Solving 27.5 + x = 30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 30.004166377 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 30.004166377 + -27.5 x = 30.004166377 + -27.5 Combine like terms: 30.004166377 + -27.5 = 2.504166377 x = 2.504166377 Simplifying x = 2.504166377

Subproblem 2

x + 27.5 = -30.004166377 Simplifying x + 27.5 = -30.004166377 Reorder the terms: 27.5 + x = -30.004166377 Solving 27.5 + x = -30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -30.004166377 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -30.004166377 + -27.5 x = -30.004166377 + -27.5 Combine like terms: -30.004166377 + -27.5 = -57.504166377 x = -57.504166377 Simplifying x = -57.504166377

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.504166377, -57.504166377}

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