X^2-34x+100=0 solve
Gotta use the quadratic formula for this one.
or, solve by completing the square:
x^2 - 34x = -100
34/2 = 17, so
x^2 - 34x + 17^2 = 100 + 17^2
(x-17)^2 = 189
x-17 = ±√189
x = 17±√189
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To solve the quadratic equation x^2 - 34x + 100 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -34, and c = 100. Plugging these values into the quadratic formula, we get:
x = (-(-34) ± √((-34)^2 - 4(1)(100))) / (2(1))
Simplifying further:
x = (34 ± √(1156 - 400)) / 2
x = (34 ± √756) / 2
The square root of 756 can be simplified by breaking it down into factors. The factors of 756 are 2^2 * 3^3 * 7. Taking the square root of these factors, we can simplify:
√756 = √(2^2 * 3^3 * 7) = 2 * 3√7 = 6√7
Now, substituting this simplified square root back into our equation:
x = (34 ± 6√7) / 2
We can further simplify by dividing both numerator and denominator by 2:
x = (17 ± 3√7)
Therefore, the solutions to the equation x^2 - 34x + 100 = 0 are:
x = 17 + 3√7
x = 17 - 3√7