(x)=0.01x^2-6x+10

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Solution for (x)=0.01x^2-6x+10 equation:


Simplifying
(x) = 0.01x2 + -6x + 10
x = 0.01x2 + -6x + 10

Reorder the terms:
x = 10 + -6x + 0.01x2

Solving
x = 10 + -6x + 0.01x2

Solving for variable 'x'.

Reorder the terms:
-10 + x + 6x + -0.01x2 = 10 + -6x + 0.01x2 + -10 + 6x + -0.01x2

Combine like terms: x + 6x = 7x
-10 + 7x + -0.01x2 = 10 + -6x + 0.01x2 + -10 + 6x + -0.01x2

Reorder the terms:
-10 + 7x + -0.01x2 = 10 + -10 + -6x + 6x + 0.01x2 + -0.01x2

Combine like terms: 10 + -10 = 0
-10 + 7x + -0.01x2 = 0 + -6x + 6x + 0.01x2 + -0.01x2
-10 + 7x + -0.01x2 = -6x + 6x + 0.01x2 + -0.01x2

Combine like terms: -6x + 6x = 0
-10 + 7x + -0.01x2 = 0 + 0.01x2 + -0.01x2
-10 + 7x + -0.01x2 = 0.01x2 + -0.01x2

Combine like terms: 0.01x2 + -0.01x2 = 0.00
-10 + 7x + -0.01x2 = 0.00

Begin completing the square.  Divide all terms by
-0.01 the coefficient of the squared term: 

Divide each side by '-0.01'.
1000 + -700x + x2 = 0

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + -700x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + -700x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + -700x + x2 = 0 + -1000
-700x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
-700x + x2 = -1000

The x term is -700x.  Take half its coefficient (-350).
Square it (122500) and add it to both sides.

Add '122500' to each side of the equation.
-700x + 122500 + x2 = -1000 + 122500

Reorder the terms:
122500 + -700x + x2 = -1000 + 122500

Combine like terms: -1000 + 122500 = 121500
122500 + -700x + x2 = 121500

Factor a perfect square on the left side:
(x + -350)(x + -350) = 121500

Calculate the square root of the right side: 348.568501159

Break this problem into two subproblems by setting 
(x + -350) equal to 348.568501159 and -348.568501159.

Subproblem 1

x + -350 = 348.568501159 Simplifying x + -350 = 348.568501159 Reorder the terms: -350 + x = 348.568501159 Solving -350 + x = 348.568501159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '350' to each side of the equation. -350 + 350 + x = 348.568501159 + 350 Combine like terms: -350 + 350 = 0 0 + x = 348.568501159 + 350 x = 348.568501159 + 350 Combine like terms: 348.568501159 + 350 = 698.568501159 x = 698.568501159 Simplifying x = 698.568501159

Subproblem 2

x + -350 = -348.568501159 Simplifying x + -350 = -348.568501159 Reorder the terms: -350 + x = -348.568501159 Solving -350 + x = -348.568501159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '350' to each side of the equation. -350 + 350 + x = -348.568501159 + 350 Combine like terms: -350 + 350 = 0 0 + x = -348.568501159 + 350 x = -348.568501159 + 350 Combine like terms: -348.568501159 + 350 = 1.431498841 x = 1.431498841 Simplifying x = 1.431498841

Solution

The solution to the problem is based on the solutions from the subproblems. x = {698.568501159, 1.431498841}

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