Questions: Use the quadratic formula to solve for x. 2x^2+5x=4 Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. x=

Use the quadratic formula to solve for x. 2x^2+5x=4 Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. x=
Transcript text: Use the quadratic formula to solve for $x$. \[ 2 x^{2}+5 x=4 \] Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. \[ x= \]
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Solution

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Solution Steps

Step 1: Identify the coefficients

The coefficients are \(a = 2\), \(b = 5\), and \(c = -4\).

Step 2: Calculate the discriminant

The discriminant \(\Delta\) is calculated as \(b^2 - 4ac = 5^2 - 4_2_-4 = 57\). Since \(\Delta > 0\), there are two distinct real solutions.

Step 3: Apply the quadratic formula

The solutions are calculated using the formula \(x = \frac{-b \pm \sqrt{\Delta}}{2a}\). Thus, the solutions are \(x_1 = 0.64\) and \(x_2 = -3.14\).

Final Answer:

The solutions to the quadratic equation \(ax^2 + bx + c = 0\) are \(x_1 = 0.64\) and \(x_2 = -3.14\).

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