Which of the following is a solution to the quadratic equation 2x2−5x=6 ? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point) Responses x=1.03 x equals 1.03 x=0.89 x equals 0.89 x=−0.89 x equals negative 0.89 x=−1.03
To find the solutions to the quadratic equation 2x^2 - 5x = 6, we can rearrange the equation to form:
2x^2 - 5x - 6 = 0
Next, we can solve this equation using factoring, completing the square, or using the quadratic formula. For simplicity, let's use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = -5, and c = -6. Substituting these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4(2)(-6))) / (2(2))
Simplifying further:
x = (5 ± √(25 + 48)) / 4
x = (5 ± √73) / 4
Rounding these values to the nearest hundredth:
x = (5 + √73) / 4 ≈ 1.03
x = (5 - √73) / 4 ≈ -0.89
Therefore, the solutions to the quadratic equation 2x^2 - 5x = 6 are approximately x = 1.03 and x = -0.89.
To find the solutions to the quadratic equation 2x^2 - 5x = 6, we need to set the equation equal to zero and solve for x.
Step 1: Rearrange the equation to bring all terms to one side:
2x^2 - 5x - 6 = 0
Step 2: Factor the quadratic equation, if possible. In this case, the equation cannot be factored easily.
Step 3: Use the quadratic formula to find the solutions:
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = -5, and c = -6. Plugging these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4 * 2 * (-6))) / (2 * 2)
x = (5 ± √(25 + 48)) / 4
x = (5 ± √73) / 4
Step 4: Evaluate the solutions to the quadratic equation:
Now we can calculate the values of x by rounding to the nearest hundredth.
x ≈ (5 + √73) / 4 ≈ 1.03
x ≈ (5 - √73) / 4 ≈ -1.03
So, the correct solutions, rounded to the nearest hundredth, are:
x ≈ 1.03 and x ≈ -1.03
Out of the given choices, the correct answer is x = 1.03.
To find the solution to the quadratic equation 2x^2 - 5x = 6, we can rearrange it in standard form as follows: 2x^2 - 5x - 6 = 0.
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a = 2, b = -5, and c = -6.
Plugging these values into the quadratic formula, we have:
x = (-(-5) ± √((-5)^2 - 4(2)(-6)) / (2(2))
= (5 ± √(25 + 48)) / 4
= (5 ± √73) / 4
Rounding these solutions to the nearest hundredth, we have:
x ≈ 1.03 and x ≈ -1.03
So, the correct solutions to the quadratic equation are x = 1.03 and x = -1.03.