Question
solve 3𝑥^2 + 1 = 5𝑥 − 3 using 𝑥 =−𝑏±√𝑏^2−4𝑎𝑐/ 2a and find approximate answers
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GPT 3.5
To solve the equation 3𝑥^2 + 1 = 5𝑥 − 3 using the quadratic formula 𝑥 = (-𝑏±√(𝑏^2−4𝑎𝑐)) / (2𝑎), we need to rewrite the equation in the form 𝑎𝑥^2 + 𝑏𝑥 + 𝑐 = 0.
In this case, 𝑎 = 3, 𝑏 = -5, and 𝑐 = -4.
Now, we can substitute these values into the quadratic formula:
𝑥 = (-(-5)±√((-5)^2-4(3)(-4))) / (2(3))
Simplifying further:
𝑥 = (5±√(25+48)) / 6
𝑥 = (5±√73) / 6
These are the exact solutions to the equation. To find the approximate answers, we can use a calculator to evaluate the square root and then divide by 6:
𝑥 ≈ (5+√73) / 6 ≈ 1.537
𝑥 ≈ (5-√73) / 6 ≈ -0.204
Therefore, the approximate solutions to the equation are 𝑥 ≈ 1.537 and 𝑥 ≈ -0.204.
In this case, 𝑎 = 3, 𝑏 = -5, and 𝑐 = -4.
Now, we can substitute these values into the quadratic formula:
𝑥 = (-(-5)±√((-5)^2-4(3)(-4))) / (2(3))
Simplifying further:
𝑥 = (5±√(25+48)) / 6
𝑥 = (5±√73) / 6
These are the exact solutions to the equation. To find the approximate answers, we can use a calculator to evaluate the square root and then divide by 6:
𝑥 ≈ (5+√73) / 6 ≈ 1.537
𝑥 ≈ (5-√73) / 6 ≈ -0.204
Therefore, the approximate solutions to the equation are 𝑥 ≈ 1.537 and 𝑥 ≈ -0.204.
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