How do you solve 2x^2 - 20 = 3x
Thank you
Is the answer -6? I think I got it
2x^2-3x-20=0
Use the quadratic formula.
To solve the equation 2x^2 - 20 = 3x, follow these steps:
Step 1: Rewrite the equation in the form 0 = ax^2 + bx + c. Move all the terms to one side of the equation, so subtracting 3x from both sides gives us 2x^2 - 3x - 20 = 0.
Step 2: Make sure the equation is in standard form (ax^2 + bx + c = 0), so rearrange the terms to have the highest degree of x on the left side. In this case, we already have it in standard form.
Step 3: Factor or use the quadratic formula to solve for x. In this case, the quadratic equation 2x^2 - 3x - 20 = 0 does not easily factor, so we will use the quadratic formula.
The quadratic formula states that for any equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 2, b = -3, and c = -20. Plugging these values into the quadratic formula:
x = (-(-3) ± √((-3)^2 - 4(2)(-20))) / (2(2))
Simplifying further:
x = (3 ± √(9 + 160)) / 4
x = (3 ± √169) / 4
Taking the square root of 169 gives us two solutions:
x = (3 + 13) / 4 = 16 / 4 = 4
x = (3 - 13) / 4 = -10 / 4 = -2.5
Therefore, the solutions to the equation 2x^2 - 20 = 3x are x = 4 and x = -2.5.