Question

Solve the equation for all values of x by completing the square. 5x^2-70x=-230

Solve this ASAP please

Answer 1

`\sf x=\pm √(3)+7`

solving step wise:

`\sf 5x^2-70x=-230`

divide the following by 5

`\sf x^2-14x=-46`

completing square

`\sf (x-(14)/(2))^2-((14)/(2))^2 =-46`

should look like this

`\sf (x-7)^2-49=-46`

simplify by changing sides

`\sf x-7=\pm √(3)`

final answer:

`\sf x=\pm √(3)+7`

Answer 2

`x=7 + √(3)`

`x=7 - √(3)`

Explanation:

Given equation:

`5x^2-70x=-230`

Divide both sides by 5:

`x^2-14x=-46`

Square half of the coefficient of
`x`:
`(-14 / 2)^2=49`
and add this to both sides:

`x^2-14x+49=-46+49`

Factor the left side and simplify the right side:

`(x-7)^2=3`

Square root both sides:

`x-7=\pm√(3)`

Add 7 to both sides:

`x=7 \pm √(3)`