Answer:
Hello! I'll be happy to help you with this question.
To simplify the expression
x√40 = x√5 + √10 into the form a + √b / 7, we need to follow these steps:
1. Express √40 as √(4*10) because 40 = 4 * 10.
2. Simplify √(4*10) to 2√10.
3. Substitute 2√10 back into the equation x√40 = x√5 + √10, giving x(2√10) = x√5 + √10.
4. Expand the left side to get 2x√10 = x√5 + √10.
5. Rearrange the equation to isolate the square roots: 2x√10 - √10 = x√5.
6. Factor out √10 on the left side: √10(2x - 1) = x√5.
7. Square both sides to eliminate the square root: 10(2x - 1)^2 = x^2 * 5.
8. Simplify the equation to get 40x^2 - 40x + 10 = 5x^2.
9. Combine like terms to form a quadratic equation: 35x^2 - 40x + 10 = 0.
10. Solve the quadratic equation for x using the quadratic formula or factoring.
11. Once you find the value of x, substitute it back into the equation x√40 = x√5 + √10 to get the final answer in the form a + √b / 7.
I hope this helps! If you need further assistance, feel free to ask.
Step-by-step explanation:
