Chapter 3 Assignment Question 20, 3.2.25 HW Score: \( 21.2 \%, 10.39 \) of 49 points Points: 0 of 1 Solve the equation. \[ x(5 x+8)=4 \]

To solve the equation \( x(5x + 8) = 4 \), first, expand the left side: \[ 5x^2 + 8x = 4. \] Now, rearrange the equation to set it to zero: \[ 5x^2 + 8x - 4 = 0. \] Next, you can use the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 5 \), \( b = 8 \), and \( c = -4 \). Calculate the discriminant: \[ b^2 - 4ac = 8^2 - 4(5)(-4) = 64 + 80 = 144. \] Now plug these values into the quadratic formula: \[ x = \frac{-8 \pm \sqrt{144}}{2(5)} = \frac{-8 \pm 12}{10}. \] Calculate the two possible values for \( x \): 1. \( x = \frac{-8 + 12}{10} = \frac{4}{10} = 0.4 \) 2. \( x = \frac{-8 - 12}{10} = \frac{-20}{10} = -2 \) Thus, the solutions to the equation \( x(5x + 8) = 4 \) are \( x = 0.4 \) and \( x = -2 \).