Question

(4x+1)-(4x+3)(4x-3) =26

Answer 1

Answer 2

Let's simplify the expression step by step:

$(4x+1) - (4x+3)(4x-3) = 26$

1. Distribute the terms inside the parentheses:

   $(4x + 1) - (16x^2 - 9) = 26$

2. Remove the parentheses:

   $4x + 1 - 16x^2 + 9 = 26$

3. Combine like terms:

   $4x + 10 - 16x^2 = 26$

4. Move all terms to one side to set the equation to zero:

   $-16x^2 + 4x + 10 - 26 = 0$

5. Combine constants:

   $-16x^2 + 4x - 16 = 0$

Now, the quadratic equation is in the form $ax^2 + bx + c = 0$, where $a = -16$, $b = 4$, and $c = -16$.

You can solve this quadratic equation using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substitute the values of $a$, $b$, and $c$:

$x = \frac{-4 \pm \sqrt{4^2 - 4(-16)(-16)}}{2(-16)}$

Simplify the expression under the square root:

$x = \frac{-4 \pm \sqrt{16 - 1024}}{-32}$

$x = \frac{-4 \pm \sqrt{-1008}}{-32}$

Since the square root of -1008 is an imaginary number, the solutions for $x$ will be complex numbers. The general form for complex numbers is $a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit ($\sqrt{-1}$).

Therefore, the solutions for $x$ are complex numbers. If you need the exact complex solutions, you can express them as $x = a + bi$ where $a$ and $b$ are real numbers.