Question

HELP MEE! 100 POINTS AND BRAINLY! GIVE ME THE STEPS, AND A GOOD ANSWER OR I WILL DELETE YOUR ANSWER AND GET MY POINTS BACK!

Answer 1

Hi there! Hopefully this helps!

Answer: 11.47(to 2 decimal places).

Isolate one of the square roots: √(2x−5) = 1 + √(x−1)

Square both sides: 2x−5 = (1 + √(x−1))^2

We have removed one square root.

Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)

Simplify: 2x−5 = 2√(x−1) + x

Subtract x from both sides:  x−5 = 2√(x−1)

Now do the "square root" thing again:

Isolate the square root:  √(x−1) = (x−5)/2

Square both sides:  x−1 = ((x−5)/2)^2

We have now successfully removed both square roots.

Let's continue with the solution.

Expand right hand side:  x−1 = (x^2 − 10x + 25)/4

Since it is a Quadratic Equation! let's put it in standard form.

Multiply by 4 to remove division:  4x−4 = x^2 − 10x + 25

Bring all to left:  4x − 4 − x^2 + 10x − 25 = 0

Combine like terms:  −x^2 + 14x − 29 = 0

Swap all signs:  x^2 − 14x + 29 = 0

Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:

2.53 and 11.47 (to 2 decimal places)

2.53: √(2×2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1. So it is not the solution.

11.47: √(2×11.47−5) − √(11.47−1) ≈ 1 Yes that one works.

Answer 2

Answer:

Solve the equation for  

x   by finding   a ,  b , and  c  of the quadratic then applying the quadratic formula.

Exact Form:

x= 7 + 2 √ 5

Decimal Form:

x = 11.47213595 …

Step-by-step explanation: