Quadratic formula
solve
9 over 8 - 2= 5 over x^2
To solve the equation: (9/8) - 2 = (5/x^2), we need to use the quadratic formula. However, before we proceed with that, let's simplify the equation:
Step 1: Simplify the left-hand side of the equation
9/8 - 2 = (9 - 16)/8 = -7/8
The equation is now: -7/8 = 5/x^2
Step 2: Cross-multiply to eliminate the fractions
(-7/8) * x^2 = 5
Step 3: Multiply both sides of the equation by 8 to get rid of the fraction:
-7 * x^2 = 40
Step 4: Divide both sides of the equation by -7 to isolate x^2:
x^2 = 40 / -7
Step 5: Simplify the right-hand side of the equation:
x^2 = -40/7
Now we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1 (coefficient of x^2 is 1), b = 0 (coefficient of x is 0), and c = (-40/7).
Plug in the values and simplify:
x = (-0 ± √(0^2 - 4(1)(-40/7))) / (2(1))
x = (± √(0 - (-160/7))) / 2
x = (± √(160/7)) / 2
x = ± (√160) / (2√7)
x = ± (4√10) / (2√7)
x = ± (2√10) / √7
So, the solutions for x are x = (2√10) / √7 and x = -(2√10) / √7.