x(x-a)-b(a+b)=0 In the given equation, a and b are constants. What are the solutions to the equation? Choose 1 answer: (A) x=-b and x=(a-b) (B) x=-b and x=(a+b) (C) x=a and x=(a-b) (D) x=a and x=(a+b)

Expand and Simplify Equation: First, we need to expand the equation to see if it can be factored easily. x(x-a) - b(a+b) = 0 x^2 - ax - ab - b^2 = 0Find Factors of Quadratic Equation: Now, we look for factors of the quadratic equation that could give us the solutions for x. We need to find two numbers that multiply to give -ab - b^2 and add up to give -a.Analyze Factorization and Sum: We notice that the two numbers that satisfy these conditions are -b and a-b because: (-b) * (a-b) = -ab + b^2 (-b) + (a-b) = -b + a - b = a - 2b However, we need the sum to be -a, not a - 2b. This indicates that we might have made a mistake in our factorization or that the equation does not factor in the way we expected.

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Algebra 1

Write linear equations in standard form

Full solution

x(x-a)-b(a+b)=0

\newline

In the given equation,

a

and

b

are constants. What are the solutions to the equation?

\newline

Choose

1

answer:

\newline

(A)

x=-b

and

x=(a-b)

\newline

(B)

x=-b

and

x=(a+b)

\newline

(C)

x=a

and

x=(a-b)

\newline

(D)

x=a

and

x=(a+b)

Expand and Simplify Equation: First, we need to expand the equation to see if it can be factored easily. $\newline$ $x(x-a) - b(a+b) = 0$ $\newline$ $x^2 - ax - ab - b^2 = 0$
Find Factors of Quadratic Equation: Now, we look for factors of the quadratic equation that could give us the solutions for $x$ . We need to find two numbers that multiply to give $-ab - b^2$ and add up to give $-a$ .
Analyze Factorization and Sum: We notice that the two numbers that satisfy these conditions are $-b$ and $a-b$ because: $\newline$ $(-b) \cdot (a-b) = -ab + b^2$ $\newline$ $(-b) + (a-b) = -b + a - b = a - 2b$ $\newline$ However, we need the sum to be $-a$ , not $a - 2b$ . This indicates that we might have made a mistake in our factorization or that the equation does not factor in the way we expected.