Solve the equation algebraically. 4√x+x=1

Answer 1

4√x + x = 1

4√x = 1 - x

16x = 1 - 2x + x²

0 = x² - 18x + 1

Can you solve for x and answer?

Answer 2

4√x + x = 1

Subtract x from both sides of the equation

4√x + x = 1

- x -x

4√x = 1 - x

Square both sides

[4√x]² = (1 - x)^{2 .} Remember that you must square each factor in a term, but square the binomial

16x = (1-x)(1-x)

16x = 1 - x - x + x²

16x = 1 - 2x + x²

Subtract 16x from each side of the equation

16x = 1 - 2x + x²

-16x - 16x

0 = 1 - 18x + x²

Rewrite the equation so that the quadratic is in descending order

0 = x² - 18x + 1 If this were factorable, you should factor it. However, since we can't factor this quadratic, you need to use another method like the quadratic formula.

X = -b ± √(b² - 4ac)

2a

x = 18 ± √[(-18)² - 4(1)(1)]

2(1)

x = 18 ± √(324 - 4)

2

x = 18 ± √320

2

x = 18 ± 17.89

2

x = 17.94 and x = 0.055