Final answer:
To solve the equation 4x^2+4x-2=7x, we rearrange it to the form 4x^2-3x-2=0, and then use the quadratic formula. Using a calculator, we find the roots and round to the nearest tenth. The positive root or the one that fits the context is the solution.
Step-by-step explanation:
To solve the equation 4x^2+4x-2=7x to the nearest tenth, we first need to bring all terms to one side of the equation to set it equal to zero. So, subtract 7x from both sides to get 4x^2 - 3x - 2 = 0.
Next, we can use the quadratic formula to find the values of x. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax^2 + bx + c = 0.
For our equation, a=4, b=-3, and c=-2. Plugging these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4(4)(-2))) / (2(4))
This simplifies to:
x = (3 ± √(9 + 32)) / 8
x = (3 ± √(41)) / 8
Calculating the roots we get two solutions for x. Only the positive root or the root that makes sense in the context is typically the valid solution. In this case, we need to use a calculator to calculate the numerical values of x and round to the nearest tenth.
Do remember to check the answer to ensure it is reasonable for the given problem.