To solve the equation, we need to isolate the square root term on one side.
Starting with the given equation:
2x - √x + 13 = 27
First, subtract 13 from both sides:
2x - √x = 14
Next, add √x to both sides:
2x = 14 + √x
To eliminate the square root, we can square both sides of the equation:
(2x)^2 = (14 + √x)^2
4x^2 = 196 + 28√x + x
Expanding the right side:
4x^2 = 196 + 28√x + x
Rearranging the terms:
4x^2 - 28√x - x - 196 = 0
To find the values of x that satisfy the equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a
For our quadratic equation: 4x^2 - 28√x - x - 196 = 0
a = 4, b = -28, c = -196
x = (-(-28) ± √((-28)^2 - 4(4)(-196)))/(2(4))
x = (28 ± √(784 + 3136))/8
x = (28 ± √(3920))/8
x = (28 ± 62.68)/8
Simplifying:
x = (28 + 62.68)/8 = 90.68/8 ≈ 11.34
x = (28 - 62.68)/8 = -34.68/8 ≈ -4.34
Out of the given values, only 9 makes the equation true.
Which of the following values of x makes the equation 2x−−√+13=27 true?
25
9
16
49
1 answer
1 answer