To determine whether the quadratic equation \(2x^2 - 2x - 10 = 0\) can be solved by grouping, let's first try to rewrite it in a form that may allow for grouping.
-
Start by simplifying the equation: \[ 2x^2 - 2x - 10 = 0 \] Divide every term by 2: \[ x^2 - x - 5 = 0 \]
-
Next, we need to consider if we can factor this equation directly or if grouping is applicable.
For factoring by grouping, we typically look for two numbers that multiply to give the constant term (-5) and add to the coefficient of the linear term (-1). The factors of -5 are:
- 1 and -5
- -1 and 5
Neither pair of factors adds up to -1, so we cannot factor this quadratic equation nicely using integers.
-
We could consider completing the square or using the quadratic formula to find the roots instead.
-
Since the equation \(x^2 - x - 5 = 0\) does not lend itself well to grouping (as evidenced by the failure to find suitable pairs of factors), we conclude that this particular quadratic equation cannot be solved by grouping.
Thus, the equation \(2x^2 - 2x - 10 = 0\) is the quadratic equation that is not solvable by grouping.