It is a quadratic equation and there are few ways to solve em
(Before we start note that the values of x in a quadratic equations are called roots or zeroes or solution)
Lets try both:
Taking terms common,
x(x-5) + 4(x-5) =0
(x-5)(x+4)=0
For this expression to be 0, either of the two numbers must be 0 since anything multiplied with 0 is 0.
So it can either be
(0)(x+4) = 0 Which is true or (x-5)(0) = 0 which is true too
When (x-5) = 0, x=5 and when (x+4) = 0 , x= -4
So we have two solutions 5,-4
{-b ± √(b² - 4ac)}/2a
Where the quadratic equation is ax² + bx +c =0,
Here a= 1, b = -1 and c = -20,
Substituting the values in the formula :
[-(-1) ± √{(-1)² - 4(1)(-20)}]/2(1)
={1 ± √(1 +80)}/2
=(1 ± √81)/2
=(1 ± 9)/2
2 answers are possible from here on,
(1 + 9)/2 and (1 - 9)/2
which are 10/2 = 5 and -8/2=-4
Look we same answer from both methods.
Suppose x3-4x = 0. To solve, factor: x3-4x = x(x2-4) = x(x+2)(x-2) = 0 Now, a product equals 0 if and only one or more of the factors equals 0, so set each factor to 0 and solve. The roots are 0,-2 and +2.
"x equals 0" is an equality, not an inequality. The question is, therefore, not consistent.
X = 1.8
x=2
5 ^x = 0 5 = root square 0 5=0
10x=x 9x=0 x=0
Suppose x3-4x = 0. To solve, factor: x3-4x = x(x2-4) = x(x+2)(x-2) = 0 Now, a product equals 0 if and only one or more of the factors equals 0, so set each factor to 0 and solve. The roots are 0,-2 and +2.
"x equals 0" is an equality, not an inequality. The question is, therefore, not consistent.
x: x2 - 81 = 0
X = 1.8
x=2
9x2-9x = 0 x2-x = 0 x(x-1) = 0 x = 1 or x = 0
5 ^x = 0 5 = root square 0 5=0
2x(3x+6) = 0 x = 0 or x = -2
x = 12
4x2+50x = 0 4x(x+12.5) = 0 x = 0 or x = -12.5
3x2-9x = 0 x(3x-9) = 0 x = 0 or x = 3