Solve the following quadratic equation. 3(x + 5)^2 = 60

2 answers:

7 0

$3(x+5)^2=60\ \ \ |:3\\\\(x+5)^2=20\iff x+5=\pm\sqrt{20}\ \ \ |-5\\\\x=-5\pm\sqrt{20}\\\\20=4\cdot5\to\sqrt{20}=\sqrt4\cdot\sqrt5=2\sqrt5\\\\Answer:\ x=-5-2\sqrt5\ \vee\ x=-5+2\sqrt5$

RoseWind [281]4 years ago

6 0

To solve this equation we could use:

$a^2-b^2=(a+b)(a-b)$

There will be:

$3(x + 5)^2 = 60\qquad|:3\\\\(x+5)^2=20\\\\(x+5)^2=\big(\sqrt{20}\big)^2\\\\ (x+5)^2=\big(\sqrt{4\cdot5}\big)^2\\\\(x+5)^2=\big(\sqrt{4}\cdot\sqrt{5}\big)^2\\\\(x+5)^2=\big(2\sqrt{5}\big)^2\\\\(x+5)^2-\big(2\sqrt{5}\big)^2=0\\\\ (x+5+2\sqrt{5})(x+5-2\sqrt{5})=0\\\\\\x+5+2\sqrt{5}=0\qquad\vee\qquad x+5-2\sqrt{5}=0\\\\\boxed{x=-5-2\sqrt{5}\qquad\vee\qquad x=-5+2\sqrt{5}}$

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Which sentence can represent the inequality x+251/1

wariber [46]

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It's all about making sense of an English statement. "half the sum" and "the sum of half" are two distinct expressions.

Additionally, "at least" and "not less than" have equivalent meanings, as do "not more than" and "at most."

It is an issue of matching the thoughts conveyed because all of the expressions are verbally expressed. That is a reading comprehension issue, not a math issue.

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In mathematics, a statement with unequal sides is referred to as an inequality. When a link leads to a non-equal comparison between two expressions or two numbers, it is referred to as an inequality in mathematics.

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4 0

2 years ago

Follow the process of completing the square to solve 2x2 + 8x - 12 = 0.

Rom4ik [11]

Please: Use "^" to denote exponentiation: <span>2x^2 + 8x - 12 = 0

Reduce this by div. every term by 2: </span><span>x^2 + 4x - 6 = 0

Here a=1, b=4 and c = -6. Square half of b, obtaining (4/2)^2 = 4, and add, and then subtract, this 4 to x^2 + 4x - 6:

</span> x^2 + 4x +4 - 4 - 6 = 0. Rewrite the square as (x+2)^2, obtaining new equation

(x+2)^2 = 10. Take the sqrt of both sides: x+2 = plus or minus sqrt(10).

Finally, solve for x: x = -2 plus or minus sqrt(10).

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