how many real solutions does -15^2 -3=2(7x^2 -1.5) have?
To find the number of real solutions, we first need to simplify the equation:
-15^2 - 3 = 2(7x^2 - 1.5)
Start by simplifying the left side:
(-15)^2 - 3 = 225 - 3 = 222
Now let's simplify the right side by distributing the 2:
2(7x^2 - 1.5) = 14x^2 - 3
So the equation becomes:
222 = 14x^2 - 3
Next, add 3 to both sides of the equation:
222 + 3 = 14x^2
225 = 14x^2
To isolate x^2, divide both sides by 14:
225/14 = x^2
15.93 ≈ x^2
Now, find the square root of both sides to solve for x:
x = ± √15.93 ≈ ±3.99
So, the equation has two real solutions: x ≈ 3.99 and x ≈ -3.99.