-0.008x^2+1.2x-45=-245

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Solution for -0.008x^2+1.2x-45=-245 equation:


Simplifying
-0.008x2 + 1.2x + -45 = -245

Reorder the terms:
-45 + 1.2x + -0.008x2 = -245

Solving
-45 + 1.2x + -0.008x2 = -245

Solving for variable 'x'.

Reorder the terms:
-45 + 245 + 1.2x + -0.008x2 = -245 + 245

Combine like terms: -45 + 245 = 200
200 + 1.2x + -0.008x2 = -245 + 245

Combine like terms: -245 + 245 = 0
200 + 1.2x + -0.008x2 = 0

Begin completing the square.  Divide all terms by
-0.008 the coefficient of the squared term: 

Divide each side by '-0.008'.
-25000 + -150x + x2 = 0

Move the constant term to the right:

Add '25000' to each side of the equation.
-25000 + -150x + 25000 + x2 = 0 + 25000

Reorder the terms:
-25000 + 25000 + -150x + x2 = 0 + 25000

Combine like terms: -25000 + 25000 = 0
0 + -150x + x2 = 0 + 25000
-150x + x2 = 0 + 25000

Combine like terms: 0 + 25000 = 25000
-150x + x2 = 25000

The x term is -150x.  Take half its coefficient (-75).
Square it (5625) and add it to both sides.

Add '5625' to each side of the equation.
-150x + 5625 + x2 = 25000 + 5625

Reorder the terms:
5625 + -150x + x2 = 25000 + 5625

Combine like terms: 25000 + 5625 = 30625
5625 + -150x + x2 = 30625

Factor a perfect square on the left side:
(x + -75)(x + -75) = 30625

Calculate the square root of the right side: 175

Break this problem into two subproblems by setting 
(x + -75) equal to 175 and -175.

Subproblem 1

x + -75 = 175 Simplifying x + -75 = 175 Reorder the terms: -75 + x = 175 Solving -75 + x = 175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 175 + 75 Combine like terms: -75 + 75 = 0 0 + x = 175 + 75 x = 175 + 75 Combine like terms: 175 + 75 = 250 x = 250 Simplifying x = 250

Subproblem 2

x + -75 = -175 Simplifying x + -75 = -175 Reorder the terms: -75 + x = -175 Solving -75 + x = -175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -175 + 75 Combine like terms: -75 + 75 = 0 0 + x = -175 + 75 x = -175 + 75 Combine like terms: -175 + 75 = -100 x = -100 Simplifying x = -100

Solution

The solution to the problem is based on the solutions from the subproblems. x = {250, -100}

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