0.8h^2-24h+250=570

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


Simplifying
0.8h2 + -24h + 250 = 570

Reorder the terms:
250 + -24h + 0.8h2 = 570

Solving
250 + -24h + 0.8h2 = 570

Solving for variable 'h'.

Reorder the terms:
250 + -570 + -24h + 0.8h2 = 570 + -570

Combine like terms: 250 + -570 = -320
-320 + -24h + 0.8h2 = 570 + -570

Combine like terms: 570 + -570 = 0
-320 + -24h + 0.8h2 = 0

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

Divide each side by '0.8'.
-400 + -30h + h2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -30h + 400 + h2 = 0 + 400

Reorder the terms:
-400 + 400 + -30h + h2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -30h + h2 = 0 + 400
-30h + h2 = 0 + 400

Combine like terms: 0 + 400 = 400
-30h + h2 = 400

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

Add '225' to each side of the equation.
-30h + 225 + h2 = 400 + 225

Reorder the terms:
225 + -30h + h2 = 400 + 225

Combine like terms: 400 + 225 = 625
225 + -30h + h2 = 625

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

Calculate the square root of the right side: 25

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

Subproblem 1

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

Subproblem 2

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

Solution

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

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