Final answer:
To solve the quadratic equation 3(x^2 - 7) - 2 = 25, we can rearrange it to get 0 on one side of the equation and then apply the quadratic formula to find the solutions: x = 4 and x = -4.
Step-by-step explanation:
To solve the quadratic equation 3(x^2 - 7) - 2 = 25, we need to rearrange it to get 0 on one side of the equation.
Starting with 3(x^2 - 7) - 2 = 25, we can simplify the equation to 3x^2 - 21 - 2 = 25.
Combining like terms, we get 3x^2 - 23 = 25.
Next, we subtract 25 from both sides to get 3x^2 - 23 - 25 = 0.
Simplifying further, we have 3x^2 - 48 = 0.
This is now in the form of a quadratic equation. To solve for x, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in the values from our equation, we get the quadratic formula as x = (-0 ± √(0^2 - 4(3)(-48))) / (2(3)).
Simplifying the equation under the square root, we have x = (-0 ± √(0 - (-576))) / 6.
Further simplifying, we get x = (± √576) / 6.
Taking the square root of 576, we have ± 24 / 6.
Simplifying the fraction, we get ± 4.
Therefore, the correct solutions to the quadratic equation are x = 4 and x = -4.