Question

2(4х-25)^2-7(4х-25)+3=0

Answer 1

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Answer 2

To solve the quadratic equation $2(4x-25)^2 - 7(4x-25) + 3 = 0$, we can follow these steps:

Step 1: Let's simplify the equation a bit by substituting $u = 4x - 25$. This will help us solve the quadratic equation more easily:

$2u^2 - 7u + 3 = 0$

Step 2: Factor the quadratic expression:

$2u^2 - 7u + 3 = (2u - 1)(u - 3) = 0$

Step 3: Now, set each factor equal to zero and solve for $u$:

$2u - 1 = 0$ or $u - 3 = 0$

Solving the first equation, $2u - 1 = 0$, gives us $u = \frac{1}{2}$.

Solving the second equation, $u - 3 = 0$, gives us $u = 3$.

Step 4: Recall that $u = 4x - 25$, so we can substitute the values of $u$ back into this equation:

For $u = \frac{1}{2}$: $4x - 25 = \frac{1}{2}$ $4x = \frac{1}{2} + 25$ $4x = \frac{51}{2}$ $x = \frac{51}{8}$

For $u = 3$: $4x - 25 = 3$ $4x = 3 + 25$ $4x = 28$ $x = 7$

Therefore, the solutions to the quadratic equation $2(4x-25)^2 - 7(4x-25) + 3 = 0$ are $x = \frac{51}{8}$ and $x = 7$.