solve for x.
1.25x^2=13
2.2(x-5)^2=3
solve for x.
1.25x^2=13
2.2(x-5)^2=3
1)
divide both sides by 25, we get
x^2=13/25
take square root
x = +/- sqrt(13/25)
sqrt means square root. example: sqrt(5) means square root of 5.
2)
The same kind of problem:
divide by 2 on both sides:
(x-5)^2 = 3/2
take square root:
x-5 = +/- sqrt(3/2)
add 5 on both sides:
answer x = 5+sqrt(3/2)
or x= 5-sqrt(3/2)
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To solve for x in 1.25x^2 = 13:
Step 1: Divide both sides of the equation by 1.25 to isolate x^2.
(1.25x^2)/1.25 = 13/1.25
x^2 = 10.4
Step 2: Take the square root of both sides to solve for x.
√(x^2) = √10.4
x = ±√10.4
So, the solutions for x in the equation 1.25x^2 = 13 are x = ±√10.4.
To solve for x in 2.2(x-5)^2 = 3:
Step 1: Divide both sides of the equation by 2.2 to isolate (x-5)^2.
[2.2(x-5)^2]/2.2 = 3/2.2
(x-5)^2 = 1.3636
Step 2: Take the square root of both sides to solve for (x-5).
√((x-5)^2) = √1.3636
x-5 = ±√1.3636
Step 3: Solve for x by adding 5 to both sides.
x-5+5 = ±√1.3636 + 5
x = 5 ± √1.3636
Therefore, the solutions for x in the equation 2.2(x-5)^2 = 3 are x = 5 ± √1.3636.