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3 years ago

5x = 3 – 2x^2 solve for a answer

Mathematics

1 answer:

Oliga [24]3 years ago

8 0

Answer:

x=1/2; x=-3

Step-by-step explanation:

2x^2+5x-3=0

(2x-1)(x+3)=0

2x-1=0; x=1/2

x=-3

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Can someone help me with one pleaseT (ToT)

uysha [10]

Answer:

Add 1 to both sides.

Multiply both sides by -2.

Add 8 to both sides.

Divide both sides by 5.

Step-by-step explanation:

Step 1

$-\dfrac{1}{2}(5x-8)-1=6\quad \quad \textsf{Write the equation.}$

Step 2

$-\dfrac{1}{2}(5x-8)=7 \quad \quad \textsf{Add 1 to both sides.}$

This is called the Addition Property of Equality. When the same number is added to both sides of an equation, the two sides remain equal.

$\implies -\dfrac{1}{2}(5x-8)-1+1=6+1$

$\implies -\dfrac{1}{2}(5x-8)=7$

Step 3

$5x-8=-14 \quad \quad \textsf{Multiply both sides by -2.}$

This is called the Multiplication Property of Equality. When both sides of an equation are multiplied by the same number, the two sides remain equal.

$\implies -2 \cdot -\dfrac{1}{2}(5x-8)=-2 \cdot 7$

$\implies 5x-8=-14$

Step 4

$5x=-6 \quad \quad \textsf{Add 8 to both sides.}$

This is called the Addition Property of Equality. When the same number is added to both sides of an equation, the two sides remain equal.

$\implies 5x-8+8=-14+8$

$\implies 5x=-6$

Step 5

$x=-\dfrac{6}{5} \quad \quad \textsf{Divide both sides by 5.}$

This is called the Division Property of Equality. When both sides of an equation are divided by the same number, the two sides remain equal.

$\implies \dfrac{5x}{5}=\dfrac{-6}{5}$

$\implies x=\dfrac{-6}{5}$

Conclusion

$\begin{aligned}-\dfrac{1}{2}(5x-8)-1 & =6 & \quad \quad& \textsf{Write the equation.}\\\\-\dfrac{1}{2}(5x-8) & =7 & & \boxed{\textsf{Add 1 to both sides.}}\\\\5x-8 & =-14 & & \boxed{\textsf{Multiply both sides by -2.}}\\\\5x & =-6 & & \boxed{\textsf{Add 8 to both sides.}}\\\\x & =-\dfrac{6}{5} & & \boxed{\textsf{Divide both sides by 5.}}\\\end{aligned}$

Learn more about Property Laws here:

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We can rearrange 3x+y=9 to look more conventional by subtracting 3x from both sides and making it y= -3x+9.

Now we want to find a line that is parallel to this and goes through the point (0,-4). We know that -3 is the slope. With this in mind, if we want the other line to be parallel then it must have the same slope so that they never intersect. This gives us one of the numbers we need for the second line.

This means our second equation is looking like; y= -3x+b. This means we need to find b (the y-intercept) but we are also given a point it must go through and this is (0,-4). We simply plug this in into our new equation we need to solve and we get ; -4 = -3(0) + b . "since 0 is the x and -4 is the y" . From this we get that b= -4. This means the equation of a line parallel is:

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