Let and be solutions to the equation shown, with . What is the value of ? 16x^2-8x-3=0

Recognize Equation Type: Recognize that the equation $ 16x^2 - 8x - 3 = 0 $ is a quadratic equation in the standard form $ ax^2 + bx + c = 0 $, where $ a = 16 $, $ b = -8 $, and $ c = -3 $.Sum of Roots Formula: Recall the sum of the roots formula for a quadratic equation $ ax^2 + bx + c = 0 $, which states that the sum of the roots $ x_1 + x_2 $ is equal to $ -\frac{b}{a} $.Apply Formula: Apply the sum of the roots formula to the given equation. Substitute $ a = 16 $ and $ b = -8 $ into the formula to find $ x_1 + x_2 $.Calculate Sum: Calculate the sum of the roots using the formula $ x_1 + x_2 = -\frac{-8}{16} $.Simplify Fraction: Simplify the fraction to get $ x_1 + x_2 = \frac{1}{2} $.

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Let $x_1$ and $x_2$ be solutions to the equation shown, with x_1 > x_2. What is the value of $x_1+x_2$ ? $16x^2-8x-3=0$

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Q. Let

x_1

and

x_2

be solutions to the equation shown, with

x_1 > x_2

. What is the value of

x_1+x_2

16x^2-8x-3=0

Recognize Equation Type: Recognize that the equation $16x^2 - 8x - 3 = 0$ is a quadratic equation in the standard form $ax^2 + bx + c = 0$ , where $a = 16$ , $b = -8$ , and $c = -3$ .
Sum of Roots Formula: Recall the sum of the roots formula for a quadratic equation $ax^2 + bx + c = 0$ , which states that the sum of the roots $x_1 + x_2$ is equal to $-\frac{b}{a}$ .
Apply Formula: Apply the sum of the roots formula to the given equation. Substitute $a = 16$ and $b = -8$ into the formula to find $x_1 + x_2$ .
Calculate Sum: Calculate the sum of the roots using the formula $x_1 + x_2 = -\frac{-8}{16}$ .
Simplify Fraction: Simplify the fraction to get $x_1 + x_2 = \frac{1}{2}$ .