Question

If anyone can help me to solve this!!​

Answer 1

`\begin{array}\cline{1-5} \textbf{Equation} & \textbf{Standard Form} & \textbf{a} & \textbf{b} & \textbf{c}\\\cline{1-5} \text{1.}\:\:x^2+x=20 & x^2+x-20=0 & 1 & 1 & -20\\\cline{1-5} \text{2.}\:\:4x^2-2x=28 \phantom{)))}& 4x^2-2x-28=0 \phantom{)))}& 4 & -2 & -28\\\cline{1-5} \text{3.}\:\:5x^2=225 & 5x^2-225=0 & 5 & 0 & -225\\\cline{1-5} \text{4.}\:\:x^2-x=36 & x^2-x-36=0 & 1 & -1 & -36\\\cline{1-5} \text{5.}\:\:3x^2-4=7x & 3x^2-7x-4=0 & 3 & -7 & -4 \\\cline{1-5}\end{array}`

Explanation:

Standard form of a quadratic equation:

`\boxed{ax^2+bx+c=0}`

Question 1

Given:

`x^2+x=20`

Rearrange to standard form by subtracting 20 from both sides:

`\implies x^2+x -20=20-20`

`\implies x^2+x -20=0`

Therefore:

• a = 1
• b = 1
• c = -20

Question 2

Given:

`4x^2-2x=28`

Rearrange to standard form by subtracting 28 from both sides:

`\implies 4x^2-2x-28=28-28`

`\implies 4x^2-2x-28=0`

Therefore:

• a = 4
• b = -2
• c = -28

Question 3

Given:

`5x^2=225`

Rearrange to standard form by subtracting 225 from both sides:

`\implies 5x^2-225=225-225`

`\implies 5x^2-225=0`

Therefore:

• a = 5
• b = 0
• c = -225

Question 4

Given:

`x^2-x=36`

Rearrange to standard form by subtracting 36 from both sides:

`\implies x^2-x-36=36-36`

`\implies x^2-x-36=0`

Therefore:

• a = 1
• b = -1
• c = -36

Question 5

Given:

`3x^2-4=7x`

Rearrange to standard form by subtracting 7x from both sides:

`\implies 3x^2-4-7x=7x-7x`

`\implies 3x^2-4-7x=0`

`\implies 3x^2-7x-4=0`

Therefore:

• a = 3
• b = -7
• c = -4