Final answer:
To solve the equation 2x² - 19x + 2 = -10x to the nearest tenth, rearrange it as a quadratic equation and use the quadratic formula to find the values of x. The two possible values are approximately 2.62 and 0.38, rounded to the nearest tenth. The answer to the nearest tenth is approximately 0.4.
Step-by-step explanation:
To solve the equation 2x² - 19x + 2 = -10x to the nearest tenth, we need to rearrange it as a quadratic equation.
By subtracting -10x from both sides, the equation becomes 2x² - 9x + 2 = 0.
Now, we can use the quadratic formula to find the values of x. The formula is x = (-b ± √(b² - 4ac)) / (2a).
Plugging in the values a = 2, b = -9, and c = 2 into the formula, we get:
x = (-(-9) ± √((-9)² - 4(2)(2))) / (2(2))
x = (9 ± √(81 - 16)) / 4
x = (9 ± √65) / 4
The two possible values for x are approximately 2.62 and 0.38, rounded to the nearest tenth.
However, since we are asked to find the value of x to the nearest tenth, the answer is approximately 0.4.