Question

Complete the steps to solve the radical equation. 7 – x = x2 + 10x + 25 0 = x2 + 11x + 18 The equation has two possible solution. What is the extraneous solution of the equation? x = What is the true solution of the equation? x =

Answer 1

There is no extraneous solution, while true solutions are x= -2 and x = -9

Step-by-step explanation:

We need to find the value of x from the equation:

$7-x = x^2 + 10x + 25$

$x^2 + 11x + 18=0$

Factorizing the equation:

$x^2 + 11x + 18=0\\x^2+9x+2x+18=0\\x(x+9)+2(x+9)=0\\(x+2)(x+9)=0\\x+2=0\,\,and\,\,x+9=0\\x=-2\,\,and\,\,x=-9$

So, values of x are: x= -2 and x = -9

Now, finding extraneous solution and true solution

Putting value of x in original equation

x= -2

$7-x = x^2 + 10x + 25$

$7-(-2) = (-2)^2 + 10(-2) + 25\\7+2=4-20+25\\9=4+5\\9=9$

Since -2 satisfies the given equation, so it is true solution.

Putting x = -9

$7-x = x^2 + 10x + 25\\7-(-9)=(-9)^2+10(-9)+25\\7+9=81-90+25\\16=16$

Since -9 satisfies the given equation, so it is true solution.

So, There is no extraneous solution, while true solutions are x= -2 and x = -9

Keywords: solve the radical equation

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Answer 2

Answer:

A. -9

B. -2

Step-by-step explanation: