When seven times a number is added to the square of the number the result is 18. Find the number.
Let X = the number.
7X + X^2 = 18
Rearrange to
X^2 + 7X -18 = 0
Solve for X.
You will get two answers, one positive and one negative. Both will satisfy the equation.
X=6 and X=1
Let's solve this step-by-step:
Let's assume the number to be 'x'.
According to the given information, seven times the number added to the square of the number is equal to 18.
So, we can write the equation as:
7x + x^2 = 18
Now, let's simplify this equation:
x^2 + 7x = 18
Rearranging the equation, we get:
x^2 + 7x - 18 = 0
Now, let's factorize the quadratic equation:
(x + 9)(x - 2) = 0
Setting each factor equal to zero, we get two possible solutions:
1. x + 9 = 0, which gives x = -9
2. x - 2 = 0, which gives x = 2
Therefore, the possible solutions for the number are x = -9 and x = 2.
To find the number, we can set up an equation based on the given information.
Let's assume the number is "x."
According to the given information, seven times the number "x" is added to the square of the number "x," resulting in 18. Mathematically, this can be expressed as:
7x + x^2 = 18
To solve this quadratic equation, we can rearrange it into the standard form:
x^2 + 7x - 18 = 0
Now, we need to factor the quadratic equation or use the quadratic formula to find the solutions for "x."
Factoring:
To factor the quadratic equation, we need to find two numbers whose product is -18 (coefficient of x^2 term multiplied by the constant term) and whose sum is 7 (coefficient of x term):
The numbers that satisfy these conditions are:
(-2) and (9)
So, we can factor the quadratic equation as follows:
(x - 2)(x + 9) = 0
By setting each factor equal to zero, we can solve for "x":
x - 2 = 0 ---> x = 2
or
x + 9 = 0 ---> x = -9
Therefore, the possible numbers that satisfy the given equation are 2 and -9.