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yuradex [85]
3 years ago
9

Solve the quadratic equation 2x^2+13x=15 by method of completing the square​

Chemistry
1 answer:
mafiozo [28]3 years ago
4 0

Answer:

x = 1, -7.5

Explanation:

2x² + 13x = 15

Divide the left side of the equation by 2

2(x² + 6.5x) = 15

Divide 6.5 by 2 and square the quotient

6.5/2 = 3.25

3.25² = 10.5625

Add 10.5625 to the left side

2(x² + 6.5x + 10.5625) = 15

Since you have a 2 outside the parentheses, you will be adding 10.5625•2 to the right side.

10.5625 • 2 = 21.125

2(x² + 6.5x + 10.5625) = 36.125

To factor (x² + 6.5x + 10.5625), add b/2 to x

b/2 = 6.5/2 = 3.25

2(x + 3.25)² = 36.125

Divide by 2

(x + 3.25)² = 18.0625

Square root.

(x + 3.25) = √18.0625

x + 3.25 = ±4.25

Subtract 3.25.

x = 4.25 - 3.25 = 1

x = -4.25 - 3.25 = -7.5

x = 1, -7.5

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Based on the equation, how many grams of Br2 are required to react completely with 36.2 grams of AlCl3?
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Answer:

65.08 g.

Explanation:

  • For the reaction, the balanced equation is:

<em>2AlCl₃ + 3Br₂ → 2AlBr₃ + 3Cl₂,</em>

2.0 mole of AlCl₃ reacts with 3.0 mole of Br₂ to produce 2.0 mole of AlBr₃ and 3.0 mole of Cl₂.

  • Firstly, we need to calculate the no. of moles of 36.2 grams of AlCl₃:

<em>n = mass/molar mass</em> = (36.2 g)/(133.34 g/mol) = <em>0.2715 mol.</em>

<u><em>Using cross multiplication:</em></u>

2.0 mole of AlCl₃ reacts with → 3.0 mole of Br₂, from the stichiometry.

0.2715 mol of AlCl₃ reacts with → ??? mole of Br₂.

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3 years ago
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