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If 2x^2 + 3x - 5 = 0, what is the value of x using the quadratic formula?
If 2x^2 + 3x - 5 = 0, what is the value of x using the quadratic formula?
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Practice Questions
1 question
Q1
If 2x^2 + 3x - 5 = 0, what is the value of x using the quadratic formula?
x = 1
x = -1
x = 2
x = -2
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Using the quadratic formula x = [-b ± √(b² - 4ac)] / 2a, we find x = [-3 ± √(9 + 40)] / 4.
Questions & Step-by-step Solutions
1 item
Q
Q: If 2x^2 + 3x - 5 = 0, what is the value of x using the quadratic formula?
Solution:
Using the quadratic formula x = [-b ± √(b² - 4ac)] / 2a, we find x = [-3 ± √(9 + 40)] / 4.
Steps: 11
Show Steps
Step 1: Identify the coefficients a, b, and c from the equation 2x^2 + 3x - 5 = 0. Here, a = 2, b = 3, and c = -5.
Step 2: Write down the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a.
Step 3: Calculate b²: b² = 3² = 9.
Step 4: Calculate 4ac: 4ac = 4 * 2 * (-5) = -40.
Step 5: Calculate b² - 4ac: 9 - (-40) = 9 + 40 = 49.
Step 6: Calculate the square root of (b² - 4ac): √49 = 7.
Step 7: Substitute b, √(b² - 4ac), and a into the quadratic formula: x = [-3 ± 7] / (2 * 2).
Step 8: Calculate the two possible values for x: x = [-3 + 7] / 4 and x = [-3 - 7] / 4.
Step 9: Simplify the first value: x = 4 / 4 = 1.
Step 10: Simplify the second value: x = -10 / 4 = -2.5.
Step 11: The two possible values for x are 1 and -2.5.
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