What is the positive solution of x2 - 36 = 5x?
Solution:
A quadratic equation is represented as ax2 + bx + c = 0 where a ≠ 0. The degree of a quadratic equation is equal to 2.
Given: x2 - 36 = 5x
x2 - 36 = 5x can be witten as x2 - 5x - 36 = 0 in standard form.
The quadratic formula is given by
x = [-b ± √(b2 - 4ac)] / 2a
We know that coefficient of x2 is a, coefficient of x is b and the constant is c.
For the given equation x2 - 5x - 36 = 0,
We have, a = 1, b = -5 and c = - 36
Using the quadratic formula, we get,
x = [ -(-5) ± √{(-5)2 - 4 (1) (-36)}] / 2(1)
x = [5 ± √{25 + 144}] / 2
x = (5 ± √169) / 2
x = (5 ± 13) / 2
Hence, we have two solutions:
x = (5 + 13) / 2 and, x = (5 - 13) / 2
x = 18/2 and, x = -8/2
x = 9 and, x = -4
Thus, the positive solution of x2 - 36 = 5x is 9.
What is the positive solution of x2 - 36 = 5x?
Summary:
The positive solution of x2 - 36 = 5x is 9.
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