Question

Which value for x makes the open sentence true? 7 + 6 • x = 42 + x2

Answer 1

Answer:

x has 2 values: $x_{1}=3 + \sqrt{26} *i$ , $x_{2} = 3 - \sqrt{26}*i$

Step-by-step explanation:

First: Rearrange the equation to get 0 as a result.

(In this case: $x^{2} -6x + 42-7 = 0$

that can be reduced to: $x^{2} -6x+35=0$)

Second: Apply the quadratic equation formula $x = \frac{-b±\sqrt{b^{2}-4*a*c }}{2*a}$

For a= 1 ; b= -6 ; c= 35.

Third: Replace & solve to find $x_{1}$ and $x_{2}$ :

$\frac{6±\sqrt{-104}}{2*1}$   (Note: $\sqrt{-104} = 2*\sqrt{-26}$)

And replacing $\sqrt{-1} = i$:

$x_{1} = 3+\sqrt{26}*i$ and $x_{2} = 3-\sqrt{26}*i$

Note: If a character  appears, just ignore it (it is an error in the insertion of the formulas, it has no effect on the results)

Answer 2

Answer:

The possible values of x are 3±√26i

Step-by-step explanation:

Given the equation, 7 + 6x = 42 +x², to find the value of x that makes the expression true, we need to rearrange the expression and factorize the resulting equation.

Rearranging:

7 + 6x = 42 +x²

Moving 7+6x to the other side we have:

x²+42-6x-7 = 0

x²-6x+35 =0.

Using the general formula

x = -b±√b²-4ac/2a

From the quadratic function, a = 1, b= -6, c=35

x = 6±√(-6)²-4(1)(35)/2(1)

x = 6±√36-140/2

x = 6±√-104/2

x = (6±√104×-1)/2

x = 6±√104i/2

x = 6±2√26i/2

x = 3±√26i

Note that √-1 = I (a complex value)