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3 years ago

What is the solutions of x2 = –5x + 8?

Mathematics

1 answer:

topjm [15]3 years ago

6 0

Answer:

$x=\sqrt{14.25} -2.5, x=-\sqrt{14.25}-2.5$

Step-by-step explanation:

Since moving it to one side can't be factored, I'm going to complete the square.

$x^2+5x=8$

$x^2+5x+6.25=8+6.25$

$(x+2.5)^2=14.25$

$x+2.5=\sqrt{14.25}$

$x=\sqrt{14.25} -2.5, x=-\sqrt{14.25}-2.5$

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(1/27)^x-6=27 Could I please have a step by step as well? Much appreciated!

Andrei [34K]

Answer:

$x = 7$

Step-by-step explanation:

1) Use Division Distributive Property: (x/y)^a = x^a/y^a.

$\frac{1}{ {27}^{x - 8} } = 27$

2) Multiply both sides by 27^x - 8.

$1 = {27} \times 27^{1 + x - 8}$

3) Use the product rule: x^a x^b = x^a+b.

$1 = {27}^{1 + x - 8}$

4) Simplify 1 + x - 8 to x - 7.

$1 = {27}^{x - 7}$

5) Use Definition of Common Logarithm: b^a = x if and only if logb (x) = a.

$log_{27}1 = x - 7$

6) Use Change of Base Rule.

$\frac{ log_1 }{ log{27} } = x - 7$

7) Use rule of 1: log 1 = 0.

$\frac{0}{ log_{27}} = x - 7$

8) Simplify 0/log_27 to 0.

$0 = x - 7$

9) Add 7 to both sides.

$7 = x$

10) Switch sides.

$x = 7$

Therefor, the answer is x = 7.

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