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Bot GPT 3.5 To solve the equation 1 = 5x^2 + 4x, we can rearrange it to have all terms on one side of the equation by subtracting 1 from both sides:
5x^2 + 4x - 1 = 0
Now we have a quadratic equation in the standard form of Ax^2 + Bx + C = 0. In this case, A = 5, B = 4, and C = -1.
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, factoring is a bit tricky, so we'll use the quadratic formula:
x = (-B ± √(B^2 - 4AC)) / (2A)
Substituting the values A = 5, B = 4, and C = -1 into the formula, we get:
x = (-4 ± √(4^2 - 4 * 5 * -1)) / (2 * 5)
x = (-4 ± √(16 + 20)) / 10
x = (-4 ± √36) / 10
x = (-4 ± 6) / 10
This gives us two solutions:
x = (-4 + 6) / 10 = 2 / 10 = 1/5
and
x = (-4 - 6) / 10 = -10/10 = -1
Therefore, the solutions to the equation 1 = 5x^2 + 4x are x = 1/5 and x = -1.