Question

When a number x is added to its square, the total is 12. How do you find two possible values for x?

Answer 1

x is added to its square

means

x + x² =12

x ( 1 + x) = 12

means multiplying two consecutive numbers giving 12

so 3 × 4 = 12

means x = the number = 3

and its square = 3² = 9

sum of 3 + 9 = 12

answer

Answer 2

Answer:

Value of x is -4 or 3

Step-by-step explanation:

Given,a number x is added to its square

So expression is

${x}^{2} + x$

Now given it is eqal to 12

So,

${x}^{2} + x = 12$

${x}^{2} + x - 12 = 0$

Now we want to find value of x.

By middle term, we can find value of x easily

${x}^{2} + x - (3 \times 4) = 0$

${x}^{2} + (4 - 3)x - (4 \times 3) = 0$

${x}^{2} + 4x - 3x - (3 \times 4) = 0$

$x(x + 4) - 3(x + 4) = 0$

$(x + 4)(x - 3) = 0$

We know product of two term is zero then they are separately zero

so, $(x + 4) = 0 \: \: \: \: \: or \: \: \: (x - 3) = 0$

$x = - 4 \: \: \: or \: \: + 3$