0=-.015x^2+.455x+6

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Solution for 0=-.015x^2+.455x+6 equation:


Simplifying
0 = -0.015x2 + 0.455x + 6

Reorder the terms:
0 = 6 + 0.455x + -0.015x2

Solving
0 = 6 + 0.455x + -0.015x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -0.455x + 0.015x2 = 6 + 0.455x + -0.015x2 + -6 + -0.455x + 0.015x2

Reorder the terms:
-6 + -0.455x + 0.015x2 = 6 + -6 + 0.455x + -0.455x + -0.015x2 + 0.015x2

Combine like terms: 6 + -6 = 0
-6 + -0.455x + 0.015x2 = 0 + 0.455x + -0.455x + -0.015x2 + 0.015x2
-6 + -0.455x + 0.015x2 = 0.455x + -0.455x + -0.015x2 + 0.015x2

Combine like terms: 0.455x + -0.455x = 0.000
-6 + -0.455x + 0.015x2 = 0.000 + -0.015x2 + 0.015x2
-6 + -0.455x + 0.015x2 = -0.015x2 + 0.015x2

Combine like terms: -0.015x2 + 0.015x2 = 0.000
-6 + -0.455x + 0.015x2 = 0.000

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

Divide each side by '0.015'.
-400 + -30.33333333x + x2 = 0

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -30.33333333x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -30.33333333x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -30.33333333x + x2 = 0 + 400
-30.33333333x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-30.33333333x + x2 = 400

The x term is -30.33333333x.  Take half its coefficient (-15.16666667).
Square it (230.0277779) and add it to both sides.

Add '230.0277779' to each side of the equation.
-30.33333333x + 230.0277779 + x2 = 400 + 230.0277779

Reorder the terms:
230.0277779 + -30.33333333x + x2 = 400 + 230.0277779

Combine like terms: 400 + 230.0277779 = 630.0277779
230.0277779 + -30.33333333x + x2 = 630.0277779

Factor a perfect square on the left side:
(x + -15.16666667)(x + -15.16666667) = 630.0277779

Calculate the square root of the right side: 25.100354139

Break this problem into two subproblems by setting 
(x + -15.16666667) equal to 25.100354139 and -25.100354139.

Subproblem 1

x + -15.16666667 = 25.100354139 Simplifying x + -15.16666667 = 25.100354139 Reorder the terms: -15.16666667 + x = 25.100354139 Solving -15.16666667 + x = 25.100354139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.16666667' to each side of the equation. -15.16666667 + 15.16666667 + x = 25.100354139 + 15.16666667 Combine like terms: -15.16666667 + 15.16666667 = 0.00000000 0.00000000 + x = 25.100354139 + 15.16666667 x = 25.100354139 + 15.16666667 Combine like terms: 25.100354139 + 15.16666667 = 40.267020809 x = 40.267020809 Simplifying x = 40.267020809

Subproblem 2

x + -15.16666667 = -25.100354139 Simplifying x + -15.16666667 = -25.100354139 Reorder the terms: -15.16666667 + x = -25.100354139 Solving -15.16666667 + x = -25.100354139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.16666667' to each side of the equation. -15.16666667 + 15.16666667 + x = -25.100354139 + 15.16666667 Combine like terms: -15.16666667 + 15.16666667 = 0.00000000 0.00000000 + x = -25.100354139 + 15.16666667 x = -25.100354139 + 15.16666667 Combine like terms: -25.100354139 + 15.16666667 = -9.933687469 x = -9.933687469 Simplifying x = -9.933687469

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.267020809, -9.933687469}

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