Question

consider the following quadratic equation (x+3)^2=43 when taking the square root of both sides of this equation, how many solutions will the equation have?how do you know

Answer 1

$(x + 3) {}^{2} = 43$
BY TAKING SQUARE ROOT ON BOTH SIDES

$x + 3 = \sqrt{43}$
OR
$x + 3 = - \sqrt{43}$

THUS

$x = \sqrt{43} - 3$
OR

$x = - \sqrt{43} - 3$


THIS QUADRATIC EQUATION HAS 2 SOLUTIONS SINCE √43 CAN BE A POSITIVE OR A NEGATIVE INTEGER. FOR EXAMPLE, 2^2=4
BUT, (-2)^2=4 Thus. √4=2 or (-2)

After this. Simply shifting the 3 on the LHS to keep 'x' on one side to find its value.

Answer 2

(x+3)'2=43
x+3=√43
x=-3√43 is the one solution of equation.