Answer:
Extracting Square Roots
Recall that a quadratic equation is in standard form1 if it is equal to 0 :
ax2+bx+c=0
where a,b , and c are real numbers and a≠0 . A solution to such an equation is a root of the quadratic function defined by f(x)=ax2+bx+c . Quadratic equations can have two real solutions, one real solution, or no real solution—in which case there will be two complex solutions. If the quadratic expression factors, then we can solve the equation by factoring. For example, we can solve 4x2−9=0 by factoring as follows:
4x2−9(2x+3)(2x−3)=0=0
2x+3=0 or 2x−3=02x=−32x=3x=−32x=32
The two solutions are ±32 . Here we use ± to write the two solutions in a more compact form. The goal in this section is to develop an alternative method that can be used to easily solve equations where b=0 , giving the form
ax2+c=0
The equation 4x2−9=0 is in this form and can be solved by first isolating x2 .
4x2−94x2x2=0=9=94
If we take the square root of both sides of this equation, we obtain the following:
x2−−√|x|=94−−√=32
Step-by-step explana
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