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Solve the equation $y=3x^2+5x-1$

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{36\left(x+\frac{5}{6}\right)^2-37}{12}$
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Step-by-step Solution

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  • Differential
  • Find the derivative
  • Find the integral
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
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1

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($3$) to all terms

Learn how to solve completing the square problems step by step online.

$y=3\left(x^2+\frac{5}{3}x-\frac{1}{3}\right)$

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Learn how to solve completing the square problems step by step online. Solve the equation y=3x^2+5x+-1. Use the complete the square method to factor the trinomial of the form ax^2+bx+c. Take common factor a (3) to all terms. Add and subtract \displaystyle\left(\frac{b}{2a}\right)^2. Factor the perfect square trinomial x^2+\frac{5}{3}x+\frac{25}{36}. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.

Final answer to the problem

$y=\frac{36\left(x+\frac{5}{6}\right)^2-37}{12}$

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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: $y-3x^2-5x+1$

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0
a
b
c
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:

Similar Problems Solved

$factor\left(x^3+x^2-x-1\right)$

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$factor\left(x^2-36\right)$

$factor\left(x^3-7x+6\right)$

$factor\left(x^3+2x^2-x-2\right)$

$factor\left(x^3-4x^2+x+6\right)$

Main Topic: Completing the Square

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form ax^2+bx+c to the form a(x+h)^2+k.

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