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ACT Exam  >  ACT Questions  >  If x2 - 45b2 = 4xb, what are the 2 solutions ... Start Learning for Free
If x2 - 45b2 = 4xb, what are the 2 solutions for x in terms of b?
  • a)
    15b or -3b
  • b)
    5b or -9b
  • c)
    15b or 3b
  • d)
    45b or -4b
  • e)
    9b or -5b
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
If x2 - 45b2 = 4xb, what are the 2 solutions for x in terms of b?a)15b...
The first step in answering this question is to set x2 − 45b2 = 4xb equal to zero, by isolating all of the terms on the left side:
x2 − 4xb − 45b2 = 0
The next step is to factor the equation and set each group equal to 0 in order to solve for x:
(x + 5b)(x − 9b) = 0
x + 5b = 0, so x = −5b
x − 9b = 0, so x = 9b
The two solutions for x are −5b or 9b.
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Community Answer
If x2 - 45b2 = 4xb, what are the 2 solutions for x in terms of b?a)15b...
To find the solutions for x in terms of b, we can start by rearranging the given equation:

x^2 - 45b^2 = 4xb

Now, let's solve this equation step by step:

Step 1: Move all terms to one side of the equation:

x^2 - 4xb - 45b^2 = 0

Step 2: Factor the quadratic equation:

(x - 9b)(x + 5b) = 0

Step 3: Set each factor equal to zero and solve for x:

x - 9b = 0 or x + 5b = 0

Step 4: Solve for x in each equation:

x = 9b or x = -5b

Therefore, the solutions for x in terms of b are x = 9b or x = -5b.

Explanation:
To solve the given equation, we need to rearrange it to bring all terms to one side. By subtracting 4xb from both sides of the equation, we get x^2 - 4xb - 45b^2 = 0.

Next, we factor the quadratic equation x^2 - 4xb - 45b^2 by finding two numbers that multiply to give -45b^2 and add up to -4b. These numbers are -9b and 5b, so we have (x - 9b)(x + 5b) = 0.

Setting each factor equal to zero gives us two equations: x - 9b = 0 and x + 5b = 0. Solving for x in each equation, we find x = 9b and x = -5b.

Therefore, the two solutions for x in terms of b are x = 9b and x = -5b. This means that when b takes any value, x can be calculated by multiplying that value of b by 9 or -5, respectively.
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If x2 - 45b2 = 4xb, what are the 2 solutions for x in terms of b?a)15b or -3bb)5b or -9bc)15b or 3bd)45b or -4be)9b or -5bCorrect answer is option 'E'. Can you explain this answer?
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