Question

\( 8\left[x^{2}-1\right]+6[7-x]=15 \)

Answer 1

To solve the equation 8[x² - 1] + 6[7 - x] = 15, let's distribute and simplify each term:

8(x² - 1)expands to 8x² - 8

6(7 - x) expands to 42 - 6x

Now, let's substitute these expressions back into the equation:

8x² - 8 + 42 - 6x = 15

Combine like terms:

8x² - 6x + 34 = 15

Now, bring all terms to one side to set the quadratic equation to zero:

8x² - 6x + 34 - 15 = 0

8x² - 6x + 19 = 0

Now, this is a quadratic equation. To solve it, you can use the quadratic formula:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

In this equation, (a = 8), (b = -6), and (c = 19).

x = -(-6)±√{(-6)² - 4(8)(19)}÷{2(8)}

x = 6± √{36 - 608}÷{16}

x = 6 ±√{-572}÷{16}

Since the discriminant (b² - 4ac) is negative, the solutions are complex numbers. Thus, the roots are:

x = 6±√{-572}÷{16}