Question

Solve algebraically for x: 2(x – 4) 2 + 10 = 30

Answer 1

`x=4` or
`x=2`

Explanation:

When given the following equation,

`2(x-4)^2+10=30`

One must follow the order of operations to solve the equation and get a valid result. The order of operations states the following,

1. Parenthesis

2. Exponents

3. Multiplication/ Division

4. Addition/ Subtraction.

Normally, one would combine the terms in the parenthesis, but since they are unlike terms, one will have to undo the exponents first. Expand the binomial.

`2(x-4)^2 + 10 = 30\\\\2(x^2-8x+16)+10=30`

Now distribute, multiply every term inside the parenthesis by the term outside,

`2(x^2-8x+16)+10=30\\\\2(x^2)+2(-8)x+2(16) + 10 = 30`

Simplify,

`2(x^2)+2(-8x)+2(16)+10=30`

`2x^2 -16x +32 +10 = 30`

`2x^2 -16x +42=30`

Inverse operations,

`2x^2 -16x + 42 = 30\\-30\\\\2x^2 - 16x + 12= 0`

To simplify the equation, divide all terms by (2).

`x^2 - 8x +6=0`

Factor, rewrite the quadratic equation as a product of linear equations,

`(x-4)(x-2)=0`

Solve using the zero product property. The zero product property states that any number times zero equals zero,

`(x-4)(x-2)=0\\\\x=4,x=2`