Question

Point M is the midpoint of segment AB.
AM=3x+40 and MB=x^2. Find x and AB

Answer 1

`\text{Hello there! :)}`

`x = 8\\\\AB = 128 \text{ units}`

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`\text{Since Point M is the midpoint of AB, then:}\\\\AM = MB\\\\`

`\text{Set the two equations equal to each other:}\\\\3x + 40 = x^(2) \\\\`

`\text{Move all terms over to one side to simplify more easily:}\\\\0 = x^(2) - 3x - 40`

`\text{Factor by finding numbers that sum up to -3 and multiply into -40:}\\\\0 = (x - 8)(x + 5)\\\\x = -5, 8`

`\text{The length of a segment cannot be negative, so choose the positive solution:}\\\\x = 8`

`\text{Substitute in this value of x into either AM or MB to solve for AB:}`

`AB = 2(MB)\\\\AB = 2(x^(2) )\\\\AB = 2(8^(2))\\ \\AB = 2(64)\\\\AB = 128 \text{ units}`