What is the solution to the quadratic equation 2x^2 – 5x = 6 Assume that the solution has been rounded to the nearest hundredth, if applicable.
To find the solution to the quadratic equation 2x^2 – 5x = 6, we need to rearrange the equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.
So, let's begin:
2x^2 – 5x = 6
2x^2 – 5x - 6 = 0
The equation is now in the form ax^2 + bx + c = 0, where a = 2, b = -5, c = -6.
To solve this quadratic equation, we can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 2, b = -5, and c = -6.
Let's substitute these values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4(2)(-6))) / (2(2))
x = (5 ± √(25 + 48)) / 4
x = (5 ± √73) / 4
Now, let's round these values to the nearest hundredth:
x ≈ (5 + √73) / 4 ≈ 2.37 (rounded to the nearest hundredth)
x ≈ (5 - √73) / 4 ≈ -0.87 (rounded to the nearest hundredth)
Therefore, the solution to the quadratic equation 2x^2 – 5x = 6, rounded to the nearest hundredth, is approximately x ≈ 2.37 and x ≈ -0.87.
To find the solution to the quadratic equation 2x^2 - 5x = 6, we need to use the quadratic formula. The quadratic formula states that for any quadratic equation in 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.
First, we need to substitute these values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4 * 2 * (-6))) / (2 * 2).
Simplifying further:
x = (5 ± √(25 + 48)) / 4.
x = (5 ± √73) / 4.
Now, to round the solutions to the nearest hundredth, we need to evaluate the square root (√73) and perform the division:
x ≈ (5 ± 8.54) / 4.
Simplifying further:
x₁ ≈ (5 + 8.54) / 4 ≈ 13.54 / 4 ≈ 3.39,
x₂ ≈ (5 - 8.54) / 4 ≈ -3.54 / 4 ≈ -0.88.
Therefore, the solutions to the quadratic equation 2x^2 - 5x = 6, rounded to the nearest hundredth, are approximately x₁ = 3.39 and x₂ = -0.88.
To find the solution to the quadratic equation 2x^2 - 5x = 6, we can start by rearranging the equation to have the right side equal to zero:
2x^2 - 5x - 6 = 0
Now, we can use the quadratic formula to find the solutions. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = -5, and c = -6. Substituting these values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4(2)(-6))) / (2(2))
Simplifying further:
x = (5 ± √(25 + 48)) / 4
x = (5 ± √73) / 4
Rounding to the nearest hundredth, the solutions are:
x ≈ 2.37 and x ≈ -1.37