+0

# plz help

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What is the sum of all possible values of x such that 2x(x + 10) = -50?

Jan 24, 2022

#1
+1

2x ( x + 10 ) = -50  | :2

x ( x + 10 ) = -25

x^2 + 10x = -25 | + 25

x^2 + 10x + 25 = 0

-b ± sqrt ( b^2 - 4ac )               -10 ± sqrt ( 10^2 - 4 * 1 * 25 )       -10 ± sqrt ( 100 - 100 )     -10 ± sqrt ( 0 )          -10

------------------------------     =     --------------------------------------- =  ------------------------------  =  --------------------- =  ----------- = -5 ± 0, so:

2a                                                 2                                             2                                       2                       2

x_1 = -5

x_2 = 5

( - 5 ) + 5 = 0.

The answer is 0.

Jan 24, 2022
#2
+1

2x(x + 10) = -50     expand and simplify to

2x^2 + 20x + 50 = 0   or

x^2 + 10x + 25 =0

(x+5)(x+5) = 0     shows only one root x = - 5    (a 'double root')

sum = -5

Jan 24, 2022
#3
+2

2x(x + 10) = -50

2x^2 + 20x = -50

2x^2 + 20x + 50 = 0

Using VIeta's formulas, the sum of roots of the quadratic ax^2 + bx + c = 0 is -b/a.

-b/a = -20/2 = -10.

(As ElectricPavlov has solved this question, the two roots are -5 and -5, which sum to -10 as expected.)

Jan 24, 2022
#4
+1

$$2x(x + 10) = -50$$

$$2x^2+20x=-50$$

$$2x^2+20x+50=-50+50$$

$$2x^2+20x+50=0$$

$$x_{1,\:2}=\frac{-20\pm \sqrt{20^2-4\cdot \:2\cdot \:50}}{2\cdot \:2}$$

$$x_{1,\:2}=\frac{-20\pm \sqrt{0}}{2\cdot \:2}$$

$$x=\frac{-20}{2\cdot \:2}$$

$$x=-5$$

so the value is -5

so -5!

hope this helps!,

XxmathguyxX

Jan 25, 2022