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Rewrite the function by completing the square. f(x)=x^2 - 4x + 70

Sagot :

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Answer:

x = 2 + i sqrt(66) or x = 2 - i sqrt(66)

Step-by-step explanation:

Solve for x:

x^2 - 4 x + 70 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 70 from both sides:

x^2 - 4 x = -70

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 4 to both sides:

x^2 - 4 x + 4 = -66

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 2)^2 = -66

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 2 = i sqrt(66) or x - 2 = -i sqrt(66)

Hint: | Look at the first equation: Solve for x.

Add 2 to both sides:

x = 2 + i sqrt(66) or x - 2 = -i sqrt(66)

Hint: | Look at the second equation: Solve for x.

Add 2 to both sides:

Answer: x = 2 + i sqrt(66) or x = 2 - i sqrt(66)

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