if 7 times a number is subtracted from the square of the number ,if the result is 30 .find the number
x = number
If 7 times a number is subtracted from the square of the number the result is 30, means:
x² - 7 x = 30
Subtract 30 to both sides.
x² - 7 x - 30 = 0
The solutions are:
x = - 3 and x = 10
Check results.
For x = - 3
x² - 7 x = ( - 3 )² - 7 ( - 3 ) = 9 + 21 = 30
For x = 10
x² - 7 x = 10² - 7 ∙ 10 = 100 - 70 = 30
Let's assume the number as "x".
According to the given information, we can write the equation:
x^2 - 7x = 30
Now, let's solve this equation to find the value of "x":
x^2 - 7x - 30 = 0
To factorize this quadratic equation, we need to find two numbers whose product is -30 and sum is -7.
After some trials, we find that the numbers are -10 and 3.
So, we can rewrite the equation as:
(x - 10)(x + 3) = 0
Now, we can apply the zero product property and set each factor equal to zero:
x - 10 = 0 or x + 3 = 0
Solving each equation, we find:
x = 10 or x = -3
Therefore, the possible values for the number are 10 and -3.
Let's solve the equation step by step to find the number:
Step 1: Let's assume the number is represented by 'x'.
Step 2: According to the problem, we need to subtract 7 times the number (7x) from the square of the number (x^2). This can be written as:
x^2 - 7x
Step 3: The equation given in the problem states that the result of subtracting 7 times the number from the square of the number is 30. So we have the equation:
x^2 - 7x = 30
Step 4: Rearrange the equation to put it in quadratic form:
x^2 - 7x - 30 = 0
Step 5: Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's factor:
(x - 10)(x + 3) = 0
Step 6: Set each factor equal to zero and solve for 'x':
x - 10 = 0 or x + 3 = 0
Solving these equations gives us two possible solutions for 'x':
x = 10 or x = -3
Therefore, the two possible values for the number are 10 and -3.