Question

Solve equation by using the quadratic formula.

2 x squared minus 5 x = 7
a.
x = StartFraction 2 Over 7 EndFraction, negative 1
c.
x = StartFraction 7 Over 2 EndFraction, negative 1
b.
x = StartFraction 2 Over 7 EndFraction, 0
d.
x = StartFraction 2 Over 7 EndFraction, 1



Please select the best answer from the choices provided

Answer 1

The quadratic equation 2x^2 - 5x = 7 rearranges to 2x^2 - 5x - 7 = 0, and applying the quadratic formula yields the solutions x = 7/2 and x = -1. Option c is the correct answer.

Step-by-step explanation:

To solve the quadratic equation 2x^2 - 5x = 7 using the quadratic formula, we first need to rearrange it into the standard form ax^2 + bx + c = 0. This gives us 2x^2 - 5x - 7 = 0. Now we can apply the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a).

In our equation, a = 2, b = -5, and c = -7. Plugging these into the quadratic formula, we get:

x = (-(-5) ± √((-5)^2 - 4(2)(-7))) / (2(2))
x = (5 ± √(25 + 56)) / 4
x = (5 ± √81) / 4
x = (5 ± 9) / 4

So the two solutions are:

• x = (5 + 9) / 4 = 14 / 4 = 3.5 or 7/2
• x = (5 - 9) / 4 = -4 / 4 = -1

Therefore, the correct answer is x = 7/2, -1, which matches option c from the provided choices.