0=-.08x^2+1.5x+2.5

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Solution for 0=-.08x^2+1.5x+2.5 equation:


Simplifying
0 = -0.08x2 + 1.5x + 2.5

Reorder the terms:
0 = 2.5 + 1.5x + -0.08x2

Solving
0 = 2.5 + 1.5x + -0.08x2

Solving for variable 'x'.

Combine like terms: 0 + -2.5 = -2.5
-2.5 + -1.5x + 0.08x2 = 2.5 + 1.5x + -0.08x2 + -2.5 + -1.5x + 0.08x2

Reorder the terms:
-2.5 + -1.5x + 0.08x2 = 2.5 + -2.5 + 1.5x + -1.5x + -0.08x2 + 0.08x2

Combine like terms: 2.5 + -2.5 = 0.0
-2.5 + -1.5x + 0.08x2 = 0.0 + 1.5x + -1.5x + -0.08x2 + 0.08x2
-2.5 + -1.5x + 0.08x2 = 1.5x + -1.5x + -0.08x2 + 0.08x2

Combine like terms: 1.5x + -1.5x = 0.0
-2.5 + -1.5x + 0.08x2 = 0.0 + -0.08x2 + 0.08x2
-2.5 + -1.5x + 0.08x2 = -0.08x2 + 0.08x2

Combine like terms: -0.08x2 + 0.08x2 = 0.00
-2.5 + -1.5x + 0.08x2 = 0.00

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

Divide each side by '0.08'.
-31.25 + -18.75x + x2 = 0

Move the constant term to the right:

Add '31.25' to each side of the equation.
-31.25 + -18.75x + 31.25 + x2 = 0 + 31.25

Reorder the terms:
-31.25 + 31.25 + -18.75x + x2 = 0 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + -18.75x + x2 = 0 + 31.25
-18.75x + x2 = 0 + 31.25

Combine like terms: 0 + 31.25 = 31.25
-18.75x + x2 = 31.25

The x term is -18.75x.  Take half its coefficient (-9.375).
Square it (87.890625) and add it to both sides.

Add '87.890625' to each side of the equation.
-18.75x + 87.890625 + x2 = 31.25 + 87.890625

Reorder the terms:
87.890625 + -18.75x + x2 = 31.25 + 87.890625

Combine like terms: 31.25 + 87.890625 = 119.140625
87.890625 + -18.75x + x2 = 119.140625

Factor a perfect square on the left side:
(x + -9.375)(x + -9.375) = 119.140625

Calculate the square root of the right side: 10.915155748

Break this problem into two subproblems by setting 
(x + -9.375) equal to 10.915155748 and -10.915155748.

Subproblem 1

x + -9.375 = 10.915155748 Simplifying x + -9.375 = 10.915155748 Reorder the terms: -9.375 + x = 10.915155748 Solving -9.375 + x = 10.915155748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + x = 10.915155748 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + x = 10.915155748 + 9.375 x = 10.915155748 + 9.375 Combine like terms: 10.915155748 + 9.375 = 20.290155748 x = 20.290155748 Simplifying x = 20.290155748

Subproblem 2

x + -9.375 = -10.915155748 Simplifying x + -9.375 = -10.915155748 Reorder the terms: -9.375 + x = -10.915155748 Solving -9.375 + x = -10.915155748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + x = -10.915155748 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + x = -10.915155748 + 9.375 x = -10.915155748 + 9.375 Combine like terms: -10.915155748 + 9.375 = -1.540155748 x = -1.540155748 Simplifying x = -1.540155748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.290155748, -1.540155748}

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