4 years ago

Let x^2−20x=10. What values make an equivalent number sentence after completing the square?

1 answer:

7 0

100 and 110.

You would have to add 100 to both sides. This is because to complete the square, you need to take half of the x term and square it.

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If the longest side of a right triangle is 3x-4, the shortest side is x and the other side is 2x+4, find the lengths of the side

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Answer:

$Solution,\\Let~h=3x-4~,p=x~and~b=2x+4\\Then,\\h^{2} = p^{2}+b^{2}\\or, (3x-4)^{2}=x^{2}+(2x+4)^{2}\\or, 9x^{2} - 2(3x)(4) +16 = x^{2} +4x^{2}+2(4x)(4)+16\\or, 9x^{2} -24x+16 = 5x^{2}+16x+16\\or, 9x^{2}-5x^{2}-24x-16x=0\\or, 4x^2-40x = 0\\or, 4x(x-10) = 0\\i.e. x = 0~or~x=10\\$