which of the following is a solution to the quadratic equation 2x^2-5x=6? assume that the solution has been rounded to the nearest hundredth if applicable.
x=0.89
x=1.03
x=-0.89
x=-1.03
To find the solutions to the quadratic equation, we can set the equation equal to zero:
2x^2 - 5x = 6
Rearranging the terms:
2x^2 - 5x - 6 = 0
To find the solutions, we can factor or use the quadratic formula. In this case, factoring does not easily yield the solutions, so we will use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For our quadratic equation, a = 2, b = -5, and c = -6. Plugging in these values, we get:
x = (-(-5) ± sqrt((-5)^2 - 4(2)(-6))) / (2(2))
= (5 ± sqrt(25 + 48)) / 4
= (5 ± sqrt(73)) / 4
Now we can round to the nearest hundredth:
x ≈ 0.89 (rounded to the nearest hundredth)
x ≈ -1.03 (rounded to the nearest hundredth)
Therefore, the solutions to the quadratic equation 2x^2 - 5x = 6 are x ≈ 0.89 and x ≈ -1.03.
To find the solutions to the quadratic equation 2x^2 - 5x = 6, we can rearrange the equation into the standard form, which is ax^2 + bx + c = 0. In this case, a = 2, b = -5, and c = -6.
To find the solutions, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in the values, we have:
x = (-(-5) ± √((-5)^2 - 4*2*(-6))) / (2*2)
= (5 ± √(25 + 48)) / 4
= (5 ± √(73)) / 4
Since the question asks for the solutions rounded to the nearest hundredth, we can calculate those:
x = (5 + √(73)) / 4 ≈ 1.03
x = (5 - √(73)) / 4 ≈ -0.89
Therefore, the correct solutions to the quadratic equation are:
x ≈ 1.03 and x ≈ -0.89.
To find the solution to the quadratic equation 2x^2 - 5x = 6, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 2, b = -5, and c = -6. Plugging these values into the formula, we get:
x = (-(-5) ± √((-5)^2 - 4(2)(-6))) / (2(2))
Simplifying:
x = (5 ± √(25 + 48)) / 4
x = (5 ± √73) / 4
Rounding the results to the nearest hundredth:
x ≈ 0.89 and x ≈ -1.03
So, the solutions to the quadratic equation 2x^2 - 5x = 6 rounded to the nearest hundredth are:
x = 0.89
x = -1.03