Twice the square of a certain whole number added to 3 times the number makes 90 find the number ( word problem leading to quadratic equation) show the working
2x^2 + 3x - 90 = 0
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To solve this word problem, we need to translate the given information into an equation. Let's assume the certain whole number is represented by the variable 'x'.
According to the problem, "Twice the square of a certain whole number added to 3 times the number makes 90." Mathematically, this can be written as:
2x^2 + 3x = 90
Now, we have a quadratic equation. Let's rearrange it into standard form, which means setting the equation equal to zero:
2x^2 + 3x - 90 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring:
First, we look for two numbers that multiply to give -180 (product of 2x^2 and -90) and add up to 3 (coefficient of x). After considering different pairs of numbers, we find that -9 and 20 satisfy these conditions.
Therefore, we can rewrite the equation factoring the quadratic expression:
(2x - 9)(x + 10) = 0
Now, we can set each factor equal to zero and solve for 'x':
2x - 9 = 0 or x + 10 = 0
When we solve these equations, we get two possible solutions for 'x':
2x = 9 x = -10
x = 9/2
However, the problem stated that the number is a whole number. Therefore, the only valid solution is x = 9/2.
So, the number that satisfies the given conditions is 9/2 (or 4.5, if you prefer decimal form).