720=.8x^2+x

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Solution for 720=.8x^2+x equation:


Simplifying
720 = 0.8x2 + x

Reorder the terms:
720 = x + 0.8x2

Solving
720 = x + 0.8x2

Solving for variable 'x'.

Reorder the terms:
720 + -1x + -0.8x2 = x + -1x + 0.8x2 + -0.8x2

Combine like terms: x + -1x = 0
720 + -1x + -0.8x2 = 0 + 0.8x2 + -0.8x2
720 + -1x + -0.8x2 = 0.8x2 + -0.8x2

Combine like terms: 0.8x2 + -0.8x2 = 0.0
720 + -1x + -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'.
-900 + 1.25x + x2 = 0

Move the constant term to the right:

Add '900' to each side of the equation.
-900 + 1.25x + 900 + x2 = 0 + 900

Reorder the terms:
-900 + 900 + 1.25x + x2 = 0 + 900

Combine like terms: -900 + 900 = 0
0 + 1.25x + x2 = 0 + 900
1.25x + x2 = 0 + 900

Combine like terms: 0 + 900 = 900
1.25x + x2 = 900

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 900 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 900 + 0.390625

Combine like terms: 900 + 0.390625 = 900.390625
0.390625 + 1.25x + x2 = 900.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 900.390625

Calculate the square root of the right side: 30.00650971

Break this problem into two subproblems by setting 
(x + 0.625) equal to 30.00650971 and -30.00650971.

Subproblem 1

x + 0.625 = 30.00650971 Simplifying x + 0.625 = 30.00650971 Reorder the terms: 0.625 + x = 30.00650971 Solving 0.625 + x = 30.00650971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 30.00650971 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 30.00650971 + -0.625 x = 30.00650971 + -0.625 Combine like terms: 30.00650971 + -0.625 = 29.38150971 x = 29.38150971 Simplifying x = 29.38150971

Subproblem 2

x + 0.625 = -30.00650971 Simplifying x + 0.625 = -30.00650971 Reorder the terms: 0.625 + x = -30.00650971 Solving 0.625 + x = -30.00650971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -30.00650971 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -30.00650971 + -0.625 x = -30.00650971 + -0.625 Combine like terms: -30.00650971 + -0.625 = -30.63150971 x = -30.63150971 Simplifying x = -30.63150971

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.38150971, -30.63150971}

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