How do you solve #x^2-3x=-10# by completing the square?

Answer 1

Kennedy Adams

#x^2-3x=-10#

#x^2-4x+4=-x-6#

#(x-2)^2=-x-6#

#x-2=sqrt(-x-6)#

There are no practical answers because a negative number cannot have a square root.

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Answer 2

Jameson Allen

To solve the equation x^2 - 3x = -10 by completing the square, follow these steps:

Move the constant term to the other side of the equation: x^2 - 3x + 10 = 0
To complete the square, take half of the coefficient of x, square it, and add it to both sides of the equation: x^2 - 3x + (3/2)^2 = (3/2)^2 + 10
Simplify: x^2 - 3x + 9/4 = 9/4 + 10
Rewrite the left side as a perfect square trinomial and simplify the right side: (x - 3/2)^2 = 49/4
Take the square root of both sides: x - 3/2 = ± √(49/4)
Solve for x: x = 3/2 ± 7/2
Simplify: x = (3 ± 7)/2
Final solutions: x = 5/2 or x = -1/2

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.