Solve using the quadratic formula:x^2 – 2x = 15x – 10?

x²-17x+10=0
x=17±√-17²-4(1)(10)/2
x=17±√289-40/2
x=17±√249/2

x² - 2x = 15x - 10
x² - 17x = - 10
x² - 17/2x = - 10 + (- 17/2)²
x² - 17/2x = - 40/4 + 289/4
(x - 17/2)² = 249/4
x - 17/2 = 7.889867

x = 7.889867 + 8.5, x = 16.389867
x = - 7.889867+ 8.5, x = 0.610133

Answer: x = 16.389867, 0.610133

Proof (x = 14.464179):
16.389867² - 2(16.389867) = 15(16.389867) - 10
268.628 - 32.78 = 245.848 - 10
235.848 = 235.848

Proof (x = 0.610133):
0.610133² - 2(0.610133) = 15(0.610133) - 10
0.372 - 1.22 = 9.152 - 10
- 0.848 = - 0.848

x^2-2x=15x-10

x^2-17x+10=0

a=1 b=-17 c=10

-(-17)+/- sqrt -17^2-4(1)(10)/2
17+/- sqrt 289-40/2
17+/- sqrt 249/2

x^2 - 2x = 15x - 10
x^2 - 2x - 15x + 10 = 0
x^2 - 17x + 10 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -17
c = 10

x = [17 ±√(289 - 40)]/2
x = [17 ±√249]/2

∴ x = [17 ±√249]/2

x² - 2x = 15x - 10

◊ subtract 15x from both sides ◊

x² - 17x = -10

◊ add 10 to both sides ◊

x² - 17x + 10 = 0

◊ plug into the quadratic formula ◊

[-(-17) ± √((-17)² - 4(1)(10))] / 2(1)

◊ Simplify down to ◊

(17/2) ± (1/2)√249

◊ write as roots ◊

x = (17/2) - (1/2)√249 ≈ 0.6101
x = (17/2) + (1/2)√249 ≈ 16.3899

x^2 - 2x = 15x - 10
x^2 - 17x + 10 = 0

x = [ -b +/- sqrt(b^2 - 4ac) ] / [ 2a ]

x = [ 17 +/- sqrt( (-17)^2 - 4(1)(10) ) ] / [ 2(1) ]
x = [ 17 +/- sqrt( 289 - 40 ) ] / [ 2 ]
x = [ 17 +/- sqrt(249) ] / 2

x^2 - 17x + 10 = 0
x = (17+sqrt249)/2, (17-sqrt249)/2

x ² - 17 x + 10 = 0

x = [ 17 ± √ (289 - 40 ) ] / 2

x = [ 17 ± √ (249) ] / 2