Question

Solve the quadratic equation 2x^2 - 8x = -7.

a) -2(plus or minus) square root of 2
b) -2(plus or minus) 2 square root of 2
c) 2(plus or minus) square root of 2 (both) over 2
d) 2(plus or minus) square root of 2 only over 2

Answer 1

The quadratic equation 2x^2 - 8x = -7 is solved by first rearranging it into the standard form and then applying the quadratic formula to find the roots, which are x = 2 ± √(2).

Step-by-step explanation:

To solve the quadratic equation 2x^2 - 8x = -7, we first need to move all terms to one side to get the standard form of a quadratic equation ax^2 + bx + c = 0. Adding 7 to both sides of the equation we have:

2x^2 - 8x + 7 = 0

Now we use the quadratic formula, -b ± √(b^2 - 4ac) / (2a), to find the solutions for x.

Here, a = 2, b = -8, and c = 7. Plugging these values into the quadratic formula:

x = (-(-8) ± √((-8)^2 - 4(2)(7))) / (2(2))

x = (8 ± √(64 - 56)) / 4

x = (8 ± √(8)) / 4

x = (8 ± 2√(2)) / 4

We can simplify by dividing both terms in the numerator by 4:

x = (2 ± √(2))

Then, x = 2 ± √(2) are the roots of the equation.