Maths question: Solve (2x – 5)² = 7?

(2x – 5)² = 7
4x² – 20x + 25 – 7 = 0
4x² – 20x + 18 = 0
2x² – 10x + 9 = 0
x = { 10 ± Sq Root ( 100 - 72 ) } ÷ 4
= [10 ± √28]/4
= [10 ± 2√7]/4
= 5/2 ± √7/2

Method 2
(2x – 5)² = 7
(2x – 5) = ±√7
2x = 5 ± √7
x = 5/2 ± √7/2
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(2x – 5)² = 7

Expand.
(2x – 5)(2x – 5) = 7

Distribute.
2x(2x) + 2x(-5) - 5(2x) - 5(-5) = 7
4x^2 - 10x - 10x + 25 = 7
4x^2 - 20x + 18 = 0

Use the quadratic formula.
Given: ax² + bx + c = 0
Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a

Given: 4x^2 - 20x + 18 = 0
Means: a = 4, b = -20, c = 18

Plug these values into the formula.
x = [-b ± √(b² - 4ac)] / 2a
x = [-(-20) ± √((-20)² - 4(4)(18))] / 2(4)
x = [20 ± √(400 - 288)] / 8
x = [20 ± √112] / 8
x = [20 ± √(16 * 7)] / 8
x = (20 ± 4√7) / 8
x = (5 ± √7) / 2

ANSWER: x = (5 ± √7) / 2

2x - 5 = ± √7
2x = 5 ± √7
x = (1/2) (5 ± √7)

(2x-5)^2=4x^2-20x+25

4x^2-20x+25=7
subtract 7 from both sides

4x^2-20x+18=0

Put that in the quadratic formula.

solutions are given by
x=(5+/-sqrt7)/2

x=3.82
x=1.18

(2x-5)=sq root of 7
Or 2x=(sq root of 7)-5
or x=((sq root of 7)-5)/2

take square root of both sides.
2x-5=+- /7 ( root seven)
2x=+-/7+5 (plus minus root seven plus five)
x= +-/7 +5 /2 plus minus root seven plus five wholly divided by 2

sorry i dont know how to type the math symbols correctly in here

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

This has two solution because for a number,x, x^2 = (-x)^2

Solving for x1:

2x1 - 5 = sqrt(7) // + 5

2x1 = 5 + sqrt(7)

x1 = [5 - sqrt(7)] / 2

And, likewise:

x2 = [5 + sqrt(7)] / 2

there are quite a few hassle-free how you could remedy this situation, one way is to flow-multiply. So initiate by go-multiplying, ensuing in 2x(x+one million)=5(x+7), the distribute, ensuing in 2x^2+2x=5x+35, then flow all words to the left element of the equation, ensuing in 2x^2-3x-35=0, then element the equation, ensuing in (2x+7)(x-5)=0, then set up each and every volume to 0, ensuing in 2x+7=0 and x-5=0, then remedy each and every equation, ensuing in -7/2 or 5. counting on what the question asked, the two effects could be recommendations or the destructive answer might desire to be thrown out.

(2x - 5)^2 = 7
2x - 5 = ±√7
2x - 5 ≈ ±2.64

2x - 5 ≈ 2.64
2x ≈ 2.64 + 5
2x ≈ 7.64
x ≈ 7.64/2
x ≈ 3.82

2x - 5 ≈ -2.64
2x ≈ -2.64 + 5
2x ≈ 2.36
x ≈ 2.36/2
x ≈ 1.18

∴ x ≈ 1.18 , 3.82

multiply to open the square brackets

[2x-5]^2 = 4x^2 - 20x + 25 = 7

then subtract 7 from both sides to get a zero at the end

4x^2 - 20x + 25 - 7 = 4x^2 - 20x + 18 = 0

which gives the answers of x = [5 +/- sqrt7]/2

when using the quadratic formula