One number is equal to the square of another. Find the numbers if both are positive and their sum is 2450.
x = one number
2450 - x = other number {the sum of the two numbers is 2450}
2450 - x = x² {one number equals square of another}
x² + x - 2450 = 0 {subtracted 2450 from each side and added x}
(x + 50)(x - 49) = 0 {factored into two binomials}
x + 50 = 0 or x - 49 = 0 {set equal to zero}
x = -50 or x = 49 {solved each equation for x}
Only using the positive number, 49.
2450 - x = 2401 {substituted 49, in for x, into (2450 - x)}
49 and 2401 are the two numbers
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2450 - x = other number {the sum of the two numbers is 2450}
2450 - x = x² {one number equals square of another}
x² + x - 2450 = 0 {subtracted 2450 from each side and added x}
(x + 50)(x - 49) = 0 {factored into two binomials}
x + 50 = 0 or x - 49 = 0 {set equal to zero}
x = -50 or x = 49 {solved each equation for x}
Only using the positive number, 49.
2450 - x = 2401 {substituted 49, in for x, into (2450 - x)}
49 and 2401 are the two numbers
Ask Algebra House
