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postnew [5]
3 years ago
7

What value of g makes the equation true? (x+7)(x-4)=x²+gx-28

Mathematics
1 answer:
defon3 years ago
6 0

Answer:

g=3

Step-by-step explanation:

multiply x with x-4 and +7 with x-4 to open the brackets

x^2 - 4x + 7x - 28 = x^2 +gx - 28

x^2 + 3x - 28 = x^2 + gx -28

x^2 - x^2 + 3x -28 + 28 = gx

gx is kept alone on the other side because we have to find value of g

cancel out +x^2 -x^2 and +28 -28

we ll be left with

3x = gx

divide both sides by x

3x/x = gx/x

cancel out x in the numerators with the x in the denominators

3 = g

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Vaselesa [24]

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Step-by-step explanation:

x+8=±√

​86

​

​​

2 Break down the problem into these 2 equations.

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​

​​

x+8=-\sqrt{86}x+8=−√

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​

​​

3 Solve the 1st equation: x+8=\sqrt{86}x+8=√

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​

​​ .

x=\sqrt{86}-8x=√

​86

​

​​ −8

4 Solve the 2nd equation: x+8=-\sqrt{86}x+8=−√

​86

​

​​ .

x=-\sqrt{86}-8x=−√

​86

​

​​ −8

5 Collect all solutions.

x=\sqrt{86}-8,-\sqrt{86}-8x=√

​86

​

​​ −8,−√

​86

​

​​ −8

x

​2

​​ +16x−22=0

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x=\frac{-16+2\sqrt{86}}{2},\frac{-16-2\sqrt{86}}{2}x=

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​

​−16+2√

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​

​​

​​ ,

​2

​

​−16−2√

​86

​

​​

​​

3 Simplify solutions.

x=-8+\sqrt{86},-8-\sqrt{86}x=−8+√

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​

​​ ,−8−√

​86

​

​​

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