Q. Solve the quadratic by factoring.4x2−3x+12=5x+9Answer: x=
Move to Standard Form: Write the equation in standard form by moving all terms to one side of the equation.Subtract 5x and 9 from both sides of the equation 4x2−3x+12=5x+9.4x2−3x+12−5x−9=0Combine like terms.4x2−8x+3=0
Identify Coefficients: Identify a, b, and c in the standard form of the quadratic equationax2+bx+c=0.From 4x2−8x+3=0, we have:a=4b=−8c=3
Find Multiplying Numbers: Find two numbers that multiply to a∗c (4∗3=12) and add up to b (−8).We need to find two numbers that multiply to 12 and add up to −8.However, there are no two such integers that satisfy both conditions. This means the quadratic cannot be factored using integers.
Conclusion: Since the quadratic cannot be factored using integers, we can conclude that the quadratic equation does not have a solution that can be expressed as a factoring of integers. We may need to use other methods such as completing the square or the quadratic formula to find the solutions.
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