Solve x = square root of 2x - 7 + 5?

Question

The + 5 is not under the square root

Answer 1

Subtract 5 from both sides:
x - 5 = (sqrt(2x - 7)

Square both sides:
(x - 5)² = 2x - 7

Expand out the square:
x² - 10x + 25 = 2x - 7

Put everything on one side:
x² -12x + 32 = 0

Factor:
(x - 4)(x - 8) = 0

Therefore:
x = 4 or x = 8

Double-checking:
sqrt(2(4) - 7) + 5
sqrt(1) + 5
sqrt(1) is -1 or 1, so x can be 4 <-- check

sqrt(2(8) - 7) + 5
sqrt(16 - 7) + 5
sqrt(9) + 5
sqrt(9) is -3 or 3, so x can be 8 <-- check

Answer 2

x = [√(2x - 7)] + 5 --- Subtract 5 from both sides...
x - 5 = √(2x - 7) --- Square both sides...
(x - 5)² = 2x - 7
x² - 10x + 25 = 2x - 7 --- Add 7 to both sides...
x² - 10x + 32 = 2x --- Subtract 2x from each side...
x² - 12x + 32 = 0 --- Factor the left side of the equation...
(x - 8)(x - 4) = 0 --- (x - 8) and/or (x - 4) must equal 0...
x - 8 = 0 --- Add 8 to both sides...
x = 8
x - 4 = 0 --- Add 4 to both sides...
x = 4

ANSWER: x = 8 or x = 4

CHECK:
x = 8
8 = (√2(8) - 7) + 5
8 = [√(16 - 7)] + 5
8 = (√9) + 5
8 = 3 + 5
8 = 8 --- Answer checks out...

x = 4
4 = (√2(4) - 7) + 5
4 = [√(8 - 7)] + 5
4 = (√1) + 5 --- (√1) = 1 or -1, and -1 works...
4 = -1 + 5
4 = 4 --- Answer checks out...

Answer 3

First since 2x-7 is under the square root: 2x-7 >=0
Therefore x>=7/2

Equation: x=squareroot(2x-7) + 5
=> x-5=squareroot(2x-7)

=> x-5>=0 => x>=5

Square two sides: (x-5)^2=2x-7
=> x=8 or x=4 (dropped since x has to >=5)

Conclusion: x=8

Answer 4

x = √2x - 7 + 5

x - 5 = √2x - 7 + 5 - 5

(x - 5) ² = √2x - 7

x² - 10x + 25 = 2x - 7

x² - 10x + 25 - 2x = 2x - 7 - 2x

x² - 12x + 25 = - 7

x² - 12x + 25 + 7 = - 7 + 7

x² - 12x + 32 = 0

(x - 8)(x - 4)

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Roots

x = 8

x = 4

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Check

x = 8

8 = √2x - 7 + 5

8= √2(8) - 7 + 5

8 = √16 - 7 + 5

8 = √9 + 5

8 = 3 + 5

8 = 8

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The solution set { 8 }

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Answer 5

x=√(2x-7)+5 subtract 5 from each side
x-5=√(2x-7) square both sides
x^2-10x+25=2x-7 subtract RHS
x^2-12x+32=0
(x-8)(x-4)=0
x-8=0
x=8
x-4=0
x=4

x=4 does not fit. in squareing √(2x-7) we introduce the possibility that it was -√(2x-7)
x=8 is the solution
8=√(2*8-7)+5
8=√9 +5
8=3+5

Answer 6

(x-5) = sqrt(2x-7)

take square on both sides

(x-5)^2 = 2x -7

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

x^2 - 12x+32 = 0

(x-4) (x-8) = 0

so x = 4, 8

Answer 7

x - 5 = √(2x - 7)
x^2 - 10x + 25 = 2x - 7
x^2 - 12x + 32 =
(x - 4)(x - 8) = 0
x = 4, 8