Question

What are the solutions to the equation (x-1)(x+2)=-2?

Answer 1

Answer:

ײ+x-2

Step-by-step explanation:

Answer 2

Method used:-

Completing the square method.

Steps :-

$( x - 1 ) ( x + 2 ) = - 2\\x^{2}+x-2=-2 \\x^{2}+x=-2+2 \\x^{2}+x=0$

Now, make the left hand side of the equation by adding the square of ½ to both sides of the equation.

$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2} \\x^{2}+x+\frac{1}{4}=\frac{1}{4} \\\left(x+\frac{1}{2}\right)^{2}=\frac{1}{4} \\\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$

Simplify the equation. You'll get a +ve & -ve value.

$x+\frac{1}{2}=\frac{1}{2} \\x+\frac{1}{2}=-\frac{1}{2}$

Simplify it further.

$\boxed{\sf\:x=0}\\ \boxed{\sf\:x=-1 }$

The solutions are :-

x = 0 & x = -1

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Hope it helps ⚜