if 5 times a certain integer ìs subtracted from twice the square of the integer the result is 63. find the integer
You have to subtract 63 from both sides of the equation set = 0.
then factor and set each factor equal to zero to solve for x.
if five times a certain integer is subtracted from twice the square of the integer,the result is 63,find the integer
To solve this problem, let's assume that the certain integer is represented by the variable "x."
We are given that "5 times the certain integer is subtracted from twice the square of the integer, resulting in 63." This can be expressed as the equation:
2x^2 - 5x = 63
To find the integer, we need to solve this quadratic equation. Here's how:
Step 1: Rearrange the equation in standard quadratic form:
2x^2 - 5x - 63 = 0
Step 2: Factorize the quadratic equation, if possible. In this case, the equation cannot be easily factored. Therefore, we need to use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 2, b = -5, and c = -63. Plugging these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4(2)(-63))) / (2(2))
x = (5 ± √(25 + 504)) / 4
x = (5 ± √529) / 4
x = (5 ± 23) / 4
Step 3: Solve for x by considering both the positive and negative square root:
If x = (5 + 23) / 4
x = 28 / 4
x = 7
If x = (5 - 23) / 4
x = -18 / 4
x = -4.5
Therefore, the two possible integers are 7 and -4.5. However, since the problem states the integer, the solution is x = 7.
2x^2 - 5x = 63
now just solve for x