Solve the quadratic by factoring.
2, x, squared, minus, 9, x, minus, 2, equals, minus, 6
2x
2
−9x−2=−6
To solve the quadratic equation by factoring, we need to rearrange the equation to have a zero on one side:
2x^2 - 9x - 2 = -6 + 0
Simplifying the right side:
2x^2 - 9x - 2 + 6 = 0
Combining like terms:
2x^2 - 9x + 4 = 0
Now, we can factor the quadratic equation:
2x^2 - 9x + 4 = (2x - 1)(x - 4) = 0
Now, we can set each factor to zero and solve for x:
2x - 1 = 0
2x = 1
x = 1/2
x - 4 = 0
x = 4
So the solutions to the quadratic equation are x = 1/2 and x = 4.
To solve the quadratic equation by factoring:
Step 1: Rewrite the equation in the standard quadratic form: ax^2 + bx + c = 0
In this case, the equation is: 2x^2 - 9x - 2 = -6
Step 2: Move all terms to one side of the equation to set it equal to zero:
2x^2 - 9x - 2 + 6 = 0
Simplifying, we get: 2x^2 - 9x + 4 = 0
Step 3: Factor the quadratic expression.
To factor the quadratic equation 2x^2 - 9x + 4 = 0, we need to find two binomials that multiply to give us 2x^2 - 9x + 4.
We have:
(2x + 1)(x - 4) = 0
Step 4: Set each factor equal to zero and solve for x.
Setting (2x + 1) equal to zero gives:
2x + 1 = 0
2x = -1
x = -1/2
Setting (x - 4) equal to zero gives:
x - 4 = 0
x = 4
Therefore, the solutions to the quadratic equation are x = -1/2 and x = 4.
To solve the quadratic equation 2x^2 - 9x - 2 = -6 by factoring, follow these steps:
Step 1: Set the equation to zero by adding 6 to both sides to get:
2x^2 - 9x - 2 + 6 = 0
2x^2 - 9x + 4 = 0
Step 2: Factorize the quadratic expression. Look for two numbers that multiply to give the product of the coefficient of x^2 term (2) and the constant term (4), and add up to give the coefficient of the x term (-9). In this case, the numbers are -2 and -2:
(2x - 1)(x - 4) = 0
Step 3: Set each factor to zero and solve for x:
2x - 1 = 0 or x - 4 = 0
For 2x - 1 = 0:
2x = 1
x = 1/2
For x - 4 = 0:
x = 4
Therefore, the solutions to the quadratic equation 2x^2 - 9x - 2 = -6 are x = 1/2 and x = 4.