Solve the attached problem---Quadratic Equations Question: Solve for x: $2x^2 - 5x - 3 = 0$ Give your answer correct to two decimal places if necessary.

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Let's solve the quadratic equation 2x squared minus 5x minus 3 equals 0. This is a quadratic equation in standard form ax squared plus bx plus c equals 0, where a equals 2, b equals negative 5, and c equals negative 3. We'll use the quadratic formula to find the solutions. The quadratic formula is x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a. For our equation, we have a equals 2, b equals negative 5, and c equals negative 3. Let's substitute these values into the formula. Now let's substitute our values step by step. First, x equals negative of negative 5 plus or minus the square root of negative 5 squared minus 4 times 2 times negative 3, all divided by 2 times 2. This simplifies to x equals 5 plus or minus the square root of 25 plus 24, divided by 4. Next, x equals 5 plus or minus the square root of 49, divided by 4. Since the square root of 49 is 7, we get x equals 5 plus or minus 7, divided by 4. Our final answers are x equals 3 or x equals negative 0.5. Let's verify these solutions by substituting back into the original equation. For x equals 3: 2 times 3 squared minus 5 times 3 minus 3 equals 18 minus 15 minus 3, which equals 0. For x equals negative 0.5: 2 times negative 0.5 squared minus 5 times negative 0.5 minus 3 equals 0.5 plus 2.5 minus 3, which also equals 0. Both solutions check out correctly. In summary, the quadratic equation 2x squared minus 5x minus 3 equals 0 has two solutions: x equals 3 and x equals negative 0.50. These solutions represent the x-intercepts of the parabola y equals 2x squared minus 5x minus 3. As we can see in the graph, the parabola crosses the x-axis at exactly these two points, confirming our algebraic solution.