Answer:
[tex]x=4[/tex] or [tex]x=2[/tex]
Step-by-step explanation:
When given the following equation,
[tex]2(x-4)^2+10=30[/tex]
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.
[tex]2(x-4)^2 + 10 = 30\\\\2(x^2-8x+16)+10=30[/tex]
Now distribute, multiply every term inside the parenthesis by the term outside,
[tex]2(x^2-8x+16)+10=30\\\\2(x^2)+2(-8)x+2(16) + 10 = 30[/tex]
Simplify,
[tex]2(x^2)+2(-8x)+2(16)+10=30[/tex]
[tex]2x^2 -16x +32 +10 = 30[/tex]
[tex]2x^2 -16x +42=30[/tex]
Inverse operations,
[tex]2x^2 -16x + 42 = 30\\-30\\\\2x^2 - 16x + 12= 0[/tex]
To simplify the equation, divide all terms by (2).
[tex]x^2 - 8x +6=0[/tex]
Factor, rewrite the quadratic equation as a product of linear equations,
[tex](x-4)(x-2)=0[/tex]
Solve using the zero product property. The zero product property states that any number times zero equals zero,
[tex](x-4)(x-2)=0\\\\x=4,x=2[/tex]
