Which of the following is a solution to the quadratic equation 2x2−9x=4
? Assume that the solution has been rounded to the nearest hundredth. if applicable.(1 point)
Responses
x=−0.77
x equals negative 0.77
x=4.91
x equals 4.91
x=4.77
x equals 4.77
x=−0.91
To find the solution to the quadratic equation 2x^2 - 9x = 4, we need to solve for x.
Rearranging the equation, we have 2x^2 - 9x - 4 = 0.
We can use the quadratic formula to find the solutions:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = -9, and c = -4.
Using the quadratic formula, the solutions are:
x = (-(-9) ± √((-9)^2 - 4(2)(-4))) / (2(2))
= (9 ± √(81 + 32)) / 4
= (9 ± √113) / 4
Rounded to the nearest hundredth, the solutions are:
x = (-0.77, 4.91)
Therefore, the correct solution is x = -0.77 or "x equals negative 0.77".
To find the solutions to the quadratic equation 2x^2 - 9x = 4, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, the equation is 2x^2 - 9x = 4, so a = 2, b = -9, and c = -4. Let's substitute these values into the quadratic formula:
x = (-( -9) ± √((-9)^2 - 4(2)(-4))) / (2(2))
Simplifying further:
x = (9 ± √(81 + 32)) / 4
x = (9 ± √113) / 4
Now we can calculate the solutions by both adding and subtracting the square root of 113:
x1 = (9 + √113) / 4
x2 = (9 - √113) / 4
Rounding these solutions to the nearest hundredth, we get:
x1 ≈ 4.77
x2 ≈ -0.91
Therefore, the solutions to the equation 2x^2 - 9x = 4, rounded to the nearest hundredth, are:
x ≈ 4.77 and x ≈ -0.91
not the right answer
I apologize for the error in my previous response. Let's recalculate the solutions to the equation 2x^2 - 9x = 4.
Using the quadratic formula:
x = (-(-9) ± √((-9)^2 - 4(2)(-4))) / (2(2))
= (9 ± √(81 + 32)) / 4
= (9 ± √113) / 4
Rounded to the nearest hundredth:
x ≈ 4.77 and x ≈ -0.91
Therefore, the correct solutions to the equation 2x^2 - 9x = 4, rounded to the nearest hundredth, are:
x ≈ 4.77 and x ≈ -0.91
To solve the quadratic equation 2x^2 - 9x = 4, we need to rearrange it into the standard form, which is ax^2 + bx + c = 0. In this case, a = 2, b = -9, and c = -4.
To solve the equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Substituting the values, we get:
x = (-(-9) ± √((-9)^2 - 4(2)(-4))) / (2(2))
x = (9 ± √(81 + 32)) / 4
x = (9 ± √113) / 4
Now, we can calculate the solutions:
x = (9 + √113) / 4 ≈ 4.91 (rounded to the nearest hundredth)
x = (9 - √113) / 4 ≈ -0.77 (rounded to the nearest hundredth)
Therefore, the correct solution to the quadratic equation is:
x = -0.77 (rounded to the nearest hundredth)