Answer:
x = 1/5 + √(2)/5 = 0.483
or
x = 1/5 - √(2)/5 = -0.083
Step-by-step explanation:
When a math problem asks to find the "zeroes" of the equation, it is asking for the x-intercepts of the equation. In other words, you must set the equation equal to zero.
Solve for x over the real numbers:
25 x^2 - 10 x - 1 = 0
Write the quadratic equation in standard form.
Divide both sides by 25:
x^2 - 2x/5 - 1/25 = 0
Solve the quadratic equation by completing the square.
Add 1/25 to both sides:
Take one half of the coefficient of x and square it, then add it to both sides.
x^2 - 2x/5 + 1/25 = 1/25 + 1/25
Factor the left hand side.
Write the left hand side as a square:
(x - 1/5)^2 = 2/25
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 1/5 = (√2)/5 or x - 1/5 = (-√2)/5
Look at the first equation: Solve for x.
Add 1/5 to both sides:
x = 1/5 + √(2)/5 or x = 1/5 - √(2)/5
