How do you solve # 14x^2+3x-2=0#?
The solutions are
We can first factorise the equation and then find the solutions :
Factorising by splitting the middle term:
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To solve the quadratic equation 14x^2 + 3x - 2 = 0, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Where a = 14, b = 3, and c = -2. Substituting these values into the formula:
x = (-3 ± √(3^2 - 4 * 14 * -2)) / (2 * 14)
x = (-3 ± √(9 + 112)) / 28
x = (-3 ± √121) / 28
x = (-3 ± 11) / 28
So the solutions are:
x₁ = (-3 + 11) / 28 = 8/28 = 2/7 x₂ = (-3 - 11) / 28 = -14/28 = -1/2
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To solve the quadratic equation (14x^2 + 3x - 2 = 0), you can use the quadratic formula, which states that for an equation in the form (ax^2 + bx + c = 0), the solutions are given by:
[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}]
In this equation, (a = 14), (b = 3), and (c = -2). Substituting these values into the quadratic formula, we get:
[x = \frac{{-3 \pm \sqrt{{3^2 - 4 \cdot 14 \cdot (-2)}}}}{{2 \cdot 14}}]
[x = \frac{{-3 \pm \sqrt{{9 + 112}}}}{{28}}]
[x = \frac{{-3 \pm \sqrt{{121}}}}{{28}}]
[x = \frac{{-3 \pm 11}}{{28}}]
This gives two possible solutions:
[x_1 = \frac{{-3 + 11}}{{28}} = \frac{8}{28} = \frac{4}{14} = \frac{2}{7}]
[x_2 = \frac{{-3 - 11}}{{28}} = \frac{{-14}}{{28}} = -\frac{1}{2}]
So, the solutions to the equation (14x^2 + 3x - 2 = 0) are (x = \frac{2}{7}) and (x = -\frac{1}{2}).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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