Solve the equation. (Enter solutions from smallest to largest. If there is no solution, enter NONE in the answer boxes.)
5x2 = 9x + 2
5x^2 = 9x + 2
first we transpose all terms to the left side of the equation:
5x^2 - 9x - 2 = 0
then we factor (since it's factorable):
(5x + 1)(x - 2) = 0
5x + 1 = 0
5x = -1
x = -1/5
x - 2 = 0
x = 2
therefore,
x = -1/5 and x = 2
hope this helps~ XD
To solve the equation 5x^2 = 9x + 2, we will first rearrange the equation to bring all the terms to one side. In this case, let's subtract 9x and 2 from both sides of the equation:
5x^2 - 9x - 2 = 0
Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 5, b = -9, and c = -2. To find the solutions, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values for a, b, and c, we get:
x = (-(-9) ± √((-9)^2 - 4(5)(-2))) / (2(5))
x = (9 ± √(81 + 40)) / 10
x = (9 ± √121) / 10
x = (9 ± 11) / 10
Now, we have two possible solutions:
x = (9 + 11) / 10 = 20 / 10 = 2
x = (9 - 11) / 10 = -2 / 10 = -1/5
Therefore, the solutions to the equation 5x^2 = 9x + 2 are x = 2 and x = -1/5.