x^2-24x+148=12

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Solution for x^2-24x+148=12 equation:


Simplifying
x2 + -24x + 148 = 12

Reorder the terms:
148 + -24x + x2 = 12

Solving
148 + -24x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
148 + -12 + -24x + x2 = 12 + -12

Combine like terms: 148 + -12 = 136
136 + -24x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
136 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-136' to each side of the equation.
136 + -24x + -136 + x2 = 0 + -136

Reorder the terms:
136 + -136 + -24x + x2 = 0 + -136

Combine like terms: 136 + -136 = 0
0 + -24x + x2 = 0 + -136
-24x + x2 = 0 + -136

Combine like terms: 0 + -136 = -136
-24x + x2 = -136

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -136 + 144

Reorder the terms:
144 + -24x + x2 = -136 + 144

Combine like terms: -136 + 144 = 8
144 + -24x + x2 = 8

Factor a perfect square on the left side:
(x + -12)(x + -12) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -12) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + -12 = 2.828427125 Simplifying x + -12 = 2.828427125 Reorder the terms: -12 + x = 2.828427125 Solving -12 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 2.828427125 + 12 Combine like terms: -12 + 12 = 0 0 + x = 2.828427125 + 12 x = 2.828427125 + 12 Combine like terms: 2.828427125 + 12 = 14.828427125 x = 14.828427125 Simplifying x = 14.828427125

Subproblem 2

x + -12 = -2.828427125 Simplifying x + -12 = -2.828427125 Reorder the terms: -12 + x = -2.828427125 Solving -12 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -2.828427125 + 12 Combine like terms: -12 + 12 = 0 0 + x = -2.828427125 + 12 x = -2.828427125 + 12 Combine like terms: -2.828427125 + 12 = 9.171572875 x = 9.171572875 Simplifying x = 9.171572875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.828427125, 9.171572875}

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