Answer:
x = 6 or x = -3/2
Step-by-step explanation:
Solve for x:
16 x^2 - 72 x + 145 = 289
Hint: | Write the quadratic equation in standard form.
Divide both sides by 16:
x^2 - (9 x)/2 + 145/16 = 289/16
Hint: | Solve the quadratic equation by completing the square.
Subtract 145/16 from both sides:
x^2 - (9 x)/2 = 9
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 81/16 to both sides:
x^2 - (9 x)/2 + 81/16 = 225/16
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 9/4)^2 = 225/16
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 9/4 = 15/4 or x - 9/4 = -15/4
Hint: | Look at the first equation: Solve for x.
Add 9/4 to both sides:
x = 6 or x - 9/4 = -15/4
Hint: | Look at the second equation: Solve for x.
Add 9/4 to both sides:
Answer: x = 6 or x = -3/2
