2.5x^2-5x-420=0

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Solution for 2.5x^2-5x-420=0 equation:


Simplifying
2.5x2 + -5x + -420 = 0

Reorder the terms:
-420 + -5x + 2.5x2 = 0

Solving
-420 + -5x + 2.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.5'.
-168 + -2x + x2 = 0

Move the constant term to the right:

Add '168' to each side of the equation.
-168 + -2x + 168 + x2 = 0 + 168

Reorder the terms:
-168 + 168 + -2x + x2 = 0 + 168

Combine like terms: -168 + 168 = 0
0 + -2x + x2 = 0 + 168
-2x + x2 = 0 + 168

Combine like terms: 0 + 168 = 168
-2x + x2 = 168

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 168 + 1

Reorder the terms:
1 + -2x + x2 = 168 + 1

Combine like terms: 168 + 1 = 169
1 + -2x + x2 = 169

Factor a perfect square on the left side:
(x + -1)(x + -1) = 169

Calculate the square root of the right side: 13

Break this problem into two subproblems by setting 
(x + -1) equal to 13 and -13.

Subproblem 1

x + -1 = 13 Simplifying x + -1 = 13 Reorder the terms: -1 + x = 13 Solving -1 + x = 13 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 13 + 1 Combine like terms: -1 + 1 = 0 0 + x = 13 + 1 x = 13 + 1 Combine like terms: 13 + 1 = 14 x = 14 Simplifying x = 14

Subproblem 2

x + -1 = -13 Simplifying x + -1 = -13 Reorder the terms: -1 + x = -13 Solving -1 + x = -13 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -13 + 1 Combine like terms: -1 + 1 = 0 0 + x = -13 + 1 x = -13 + 1 Combine like terms: -13 + 1 = -12 x = -12 Simplifying x = -12

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14, -12}

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