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.
A. x = 0.89
B. x = -1.03
C. x = 1.03
D. x = -0.89
To find the solution to the quadratic equation 2x^2 - 5x = 6, we need to solve the equation by factoring or using the quadratic formula.
To factor the equation, start by moving all terms to one side to set the equation equal to zero:
2x^2 - 5x - 6 = 0
We can factor this quadratic equation as (2x + 3)(x - 2) = 0.
Setting each factor equal to zero, we have:
2x + 3 = 0 OR x - 2 = 0
Solving each equation separately:
2x + 3 = 0
2x = -3
x = -3/2
x = -1.5
x - 2 = 0
x = 2
So the two solutions to the quadratic equation are x = -1.5 and x = 2.
Rounded to the nearest hundredth, the solutions are:
x = -1.50 and x = 2.00
Looking at the answer choices:
A. x = 0.89 - This is not a solution to the equation.
B. x = -1.03 - This is not a solution to the equation.
C. x = 1.03 - This is not a solution to the equation.
D. x = -0.89 - This is not a solution to the equation.
None of the answer choices match the solutions to the quadratic equation.
Thus, there is no solution listed among the answer choices.
To find the solution to the quadratic equation 2x^2 - 5x = 6, we can rearrange the equation to be in standard form:
2x^2 - 5x - 6 = 0
Now we can solve this equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = -5, and c = -6. Substituting these values into the formula:
x = (-(-5) ± √((-5)^2 - 4(2)(-6))) / (2(2))
Simplifying:
x = (5 ± √(25 + 48)) / 4
x = (5 ± √73) / 4
Now let's round these solutions to the nearest hundredth:
x ≈ (5 + √73) / 4 ≈ 1.03
x ≈ (5 - √73) / 4 ≈ -0.89
Comparing these solutions to the provided options, the correct solution is:
C. x = 1.03
To find the solutions to a quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation 2x^2 - 5x = 6, let's rearrange it to match the standard form ax^2 + bx + c = 0:
2x^2 - 5x - 6 = 0
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
Now, let's round the solutions to the nearest hundredth:
x ≈ (5 + √73) / 4 ≈ 1.03
x ≈ (5 - √73) / 4 ≈ -0.89
Comparing these values with the options provided, we can see that:
A. x = 0.89 is not a solution.
B. x = -1.03 is not a solution.
C. x = 1.03 is a solution.
D. x = -0.89 is a solution.
Therefore, the correct answer is C. x = 1.03.