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Solve the equation $2x+\sqrt{x+1}=8$

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Solution

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Final answer to the problem

$x=3,\:x=\frac{21}{4}$
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Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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1

Move the term with the square root to the left side of the equation, and all other terms to the right side. Remember to change the signs of each term

Learn how to solve differential calculus problems step by step online.

$\sqrt{x+1}=8-2x$

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Learn how to solve differential calculus problems step by step online. Solve the equation 2x+(x+1)^(1/2)=8. Move the term with the square root to the left side of the equation, and all other terms to the right side. Remember to change the signs of each term. Removing the variable's exponent raising both sides of the equation to the power of 2. Factor the polynomial \left(8-2x\right) by it's greatest common factor (GCF): 2. The power of a product is equal to the product of it's factors raised to the same power.

Final answer to the problem

$x=3,\:x=\frac{21}{4}$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $2x+\sqrt{x+1}-8$

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0
a
b
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d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

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