We are required to find the unknown number from the expression
2.
let
the number = x
four times the square of a number equals 20 times that number
4x² = 20x
Divide both sides by 4x
x = 5
The number is 5
3.
let
x = the unknown number
Twice the square of the sum of a number and 3 is 98
sum of a number and 3 = x + 3
square of the sum = (x+3)²
Twice the square = 2(x + 3)²
2(x + 3)² = 98
2(x² + 6x + 9) = 98
2x² + 12x + 18 = 98
2x² + 12x +18 - 98 = 0
2x² + 12x - 80 = 0
x² + 6x - 40 = 0
using factorization method to solve the quadratic equation
x² + 10x - 4x - 40 = 0
x(x + 10) - 4(x + 10) = 0
(x + 10) ( x - 4) = 0
x + 10 = 0 or x - 4 = 0
x = -10 or x = 4
Therefore, the unknown number is -10 or 4
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