570=0.8x^2-24x+250

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Solution for 570=0.8x^2-24x+250 equation:


Simplifying
570 = 0.8x2 + -24x + 250

Reorder the terms:
570 = 250 + -24x + 0.8x2

Solving
570 = 250 + -24x + 0.8x2

Solving for variable 'x'.

Combine like terms: 570 + -250 = 320
320 + 24x + -0.8x2 = 250 + -24x + 0.8x2 + -250 + 24x + -0.8x2

Reorder the terms:
320 + 24x + -0.8x2 = 250 + -250 + -24x + 24x + 0.8x2 + -0.8x2

Combine like terms: 250 + -250 = 0
320 + 24x + -0.8x2 = 0 + -24x + 24x + 0.8x2 + -0.8x2
320 + 24x + -0.8x2 = -24x + 24x + 0.8x2 + -0.8x2

Combine like terms: -24x + 24x = 0
320 + 24x + -0.8x2 = 0 + 0.8x2 + -0.8x2
320 + 24x + -0.8x2 = 0.8x2 + -0.8x2

Combine like terms: 0.8x2 + -0.8x2 = 0.0
320 + 24x + -0.8x2 = 0.0

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
-400 + -30x + x2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -30x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -30x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -30x + x2 = 0 + 400
-30x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-30x + x2 = 400

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 400 + 225

Reorder the terms:
225 + -30x + x2 = 400 + 225

Combine like terms: 400 + 225 = 625
225 + -30x + x2 = 625

Factor a perfect square on the left side:
(x + -15)(x + -15) = 625

Calculate the square root of the right side: 25

Break this problem into two subproblems by setting 
(x + -15) equal to 25 and -25.

Subproblem 1

x + -15 = 25 Simplifying x + -15 = 25 Reorder the terms: -15 + x = 25 Solving -15 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 25 + 15 Combine like terms: -15 + 15 = 0 0 + x = 25 + 15 x = 25 + 15 Combine like terms: 25 + 15 = 40 x = 40 Simplifying x = 40

Subproblem 2

x + -15 = -25 Simplifying x + -15 = -25 Reorder the terms: -15 + x = -25 Solving -15 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -25 + 15 Combine like terms: -15 + 15 = 0 0 + x = -25 + 15 x = -25 + 15 Combine like terms: -25 + 15 = -10 x = -10 Simplifying x = -10

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40, -10}

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