PLEASE HELP!!!!!!! Solve for x. Use the completing the square method. 5x2−2x−10=0 Round decimals to the nearest tenth.

Question

asked Nov 13, 2020 63.7k views

2 Answers

Hong Van Vit · Answer 1 · 2020-11-19T16:27:43+0000

ANSWER

x=-1.2 or x=1.6

EXPLANATION

The given equation is:

$5{x}^(2) - 2x - 10 = 0$ Group and combine the constant terms:

$5{x}^(2) - 2x = 10$

Divide through by 5

${x}^(2) - (2)/(5) x = 2$

Add the square of the coefficient of x to both sides:

${x}^(2) - (2)/(5) x + (1)/(25) = 2 + (1)/(25)$

The left hand side is now a perfect square

$( {x - (1)/(5) })^(2) = (51)/(25)$

Take square root:

${x - (1)/(5) }=\pm \sqrt{(51)/(25)}$

${x = (1)/(5) }\pm ( √(51) )/(5)$

${x = (1)/(5) } - ( √(51) )/(5) \: or \: \: {x = (1)/(5) } + ( √(51) )/(5)$

x=-1.2 or x=1.6