Final answer:
To solve the equation 2x² + x = 10, we rearrange it to 2x² + x - 10 = 0 and apply the quadratic formula, resulting in two solutions: x = 2 and x = -2.5.
Step-by-step explanation:
To solve the equation 2x² + x = 10 for x, we first need to set it in standard quadratic form by moving all terms to one side, resulting in 2x² + x - 10 = 0. This can then be solved using the quadratic formula x = (-b ± √(b² - 4ac))/(2a). Now, comparing it to the general form ax² + bx + c = 0, we identify a = 2, b = 1, and c = -10.
Plugging these values into the quadratic formula, we get:
x = (-(1) ± √((1)² - 4(2)(-10)))/(2*2)
x = (-1 ± √(1 + 80))/4
x = (-1 ± √81)/4
x = (-1 ± 9)/4
This results in two solutions:
- x = (8/4) which simplifies to x = 2
- x = (-10/4) which simplifies to x = -2.5
Therefore, the equation 2x² + x = 10 has two solutions: x = 2 and x = -2.5.