10x+x^2=60

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Solution for 10x+x^2=60 equation:


Simplifying
10x + x2 = 60

Solving
10x + x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + 10x + x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 10x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 10x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 10x + x2 = 0 + 60
10x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
10x + x2 = 60

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 60 + 25

Reorder the terms:
25 + 10x + x2 = 60 + 25

Combine like terms: 60 + 25 = 85
25 + 10x + x2 = 85

Factor a perfect square on the left side:
(x + 5)(x + 5) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + 5) equal to 9.219544457 and -9.219544457.

Subproblem 1

x + 5 = 9.219544457 Simplifying x + 5 = 9.219544457 Reorder the terms: 5 + x = 9.219544457 Solving 5 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 9.219544457 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.219544457 + -5 x = 9.219544457 + -5 Combine like terms: 9.219544457 + -5 = 4.219544457 x = 4.219544457 Simplifying x = 4.219544457

Subproblem 2

x + 5 = -9.219544457 Simplifying x + 5 = -9.219544457 Reorder the terms: 5 + x = -9.219544457 Solving 5 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -9.219544457 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.219544457 + -5 x = -9.219544457 + -5 Combine like terms: -9.219544457 + -5 = -14.219544457 x = -14.219544457 Simplifying x = -14.219544457

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.219544457, -14.219544457}

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