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Hatshy [7]
3 years ago
9

What number would ypu add to both sides of x^2+7x=4 to complete the square

Mathematics
2 answers:
Tcecarenko [31]3 years ago
6 0

For a monic quadratic (factor of 1 on x^2) we always add half the coefficient on the linear (x) term, so

\left(\dfrac 7 2\right)^2 = \dfrac{49}{4}

Answer: 49/4

x^2 + 7x + \dfrac{49}{4} = 4 + \dfrac{49}{4}

(x + \frac 7 2)^2 = 4 + \frac{49}{4}


Nesterboy [21]3 years ago
3 0

(*)\qquad(a+b)^2=a^2+2ab+b^2\\\\x^2+7x=4\\\\x^2+2\cdot x\cdot3.5=4\ \ \ \ |+3.5^2\\\\\underbrace{x^2+2\cdot x\cdot3.5+3.5^2}_{(*)}=4+3.5^3\\\\(x+3.5)^2=16.25\\\\Answer:\ 3.5^2=12.25

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