How do you solve #2x^2=6x-2# using the quadratic formula?
To solve the equation (2x^2 = 6x - 2) using the quadratic formula, follow these steps:
- Rewrite the equation in standard form: (2x^2 - 6x + 2 = 0).
- Identify the coefficients: (a = 2), (b = -6), (c = 2).
- Substitute the coefficients into the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}).
- Calculate the discriminant: (b^2 - 4ac = (-6)^2 - 4(2)(2) = 36 - 16 = 20).
- Substitute the discriminant into the formula: (x = \frac{{6 \pm \sqrt{20}}}{4}).
- Simplify the square root of 20: (x = \frac{{6 \pm 2\sqrt{5}}}{4}).
- Simplify the fraction: (x = \frac{{3 \pm \sqrt{5}}}{2}).
Therefore, the solutions to the equation (2x^2 = 6x - 2) using the quadratic formula are (x = \frac{{3 + \sqrt{5}}}{2}) and (x = \frac{{3 - \sqrt{5}}}{2}).
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To solve the equation 2x^2 = 6x - 2 using the quadratic formula, follow these steps:
- Rewrite the equation in the standard form: 2x^2 - 6x + 2 = 0.
- Identify the values of coefficients a, b, and c: a = 2, b = -6, and c = 2.
- Substitute the values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
- Plug in the values: x = (-(−6) ± √((-6)^2 - 4(2)(2))) / (2(2)).
- Simplify: x = (6 ± √(36 - 16)) / 4.
- Further simplify: x = (6 ± √20) / 4.
- Split into two solutions: x = (6 + √20) / 4 and x = (6 - √20) / 4.
- Simplify the radicals if possible: x = (6 + 2√5) / 4 and x = (6 - 2√5) / 4.
- Reduce the fractions: x = (3 + √5) / 2 and x = (3 - √5) / 2.
So, the solutions to the equation 2x^2 = 6x - 2 using the quadratic formula are ( x = \frac{3 + \sqrt{5}}{2} ) and ( x = \frac{3 - \sqrt{5}}{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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