Twice the square of a certain whole number added to 3 times the number makes 90.Find the number.
15?
15^2 = 225
The number can't be 15.
Word problems leading to quadratic equation
Please help me solve this
It's 6. 2 times 6 squared is 72, 3 times 6 is 18, and 72+18=90. If you don't know algebra, you could just guess and find out what number comes out to 90. If you do, use the quadratic formula. 2x^2+3x=90 x=(-3+/-sqrt((3^2)-4*2*(-90))/(2*2)=(-3+/-sqrt(729))/4=(-3+27)/4 or (-3-27)/4=6 or -7.5, and -7.5 isn't a whole number but 6 is.
To solve this problem, let's express the problem algebraically:
Let's say the certain whole number is represented by the variable 'x'.
We know that twice the square of the number is 2x^2, and three times the number is 3x.
According to the problem, the sum of these two quantities makes 90:
2x^2 + 3x = 90
To find the value of 'x', we need to solve this equation.
Step 1: Rearrange the equation.
2x^2 + 3x - 90 = 0
Step 2: Factor the quadratic equation, if possible. In this case, factoring may not be straightforward, so we can use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = 3, and c = -90.
Step 3: Substitute the values into the quadratic formula and solve for 'x'.
x = (-3 ± √(3^2 - 4*2*(-90))) / (2*2)
= (-3 ± √(9 + 720)) / 4
= (-3 ± √729) / 4
Since √729 = 27, we have two possible solutions:
x = (-3 + 27) / 4 = 6
x = (-3 - 27) / 4 = -7.5
However, as the problem states that the number is a whole number, the solution is x = 6.
Therefore, the number is 6.