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navik [9.2K]
2 years ago
9

Solve by completing the square. Round your answers to the nearest tenth and then locate the greater solution.

tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class="latex-formula">+10x-7=0
Mathematics
1 answer:
Andrews [41]2 years ago
3 0

Step-by-step explanation:

Step 1: Write our Givens

{x}^{2}  + 10x - 7 = 0

Move the constant term ,(the term with no variable) to the right side.

Here we have a negative 7, so we add 7 to both sides

{x}^{2}  + 10x = 7

Next, we take the linear coeffeicent and divide it by 2 then square it.

( \frac{10}{2} ) {}^{2}  = 25

Then we add that to both sides

{x}^{2}  + 10x + 25 = 7 + 25

{ {x}^{2} } + 10x + 25 = 32

Next, we factor the left,

(x + 5)(x + 5) = 32

we got 5 because 5 add to 10 and multiply to 25 as well.

so we get

(x + 5) {}^{2}  = 32

This is called a perfect square trinomial.

Next, we take the square root of both sides

x + 5 = ± \sqrt{32}

± menas that we have a positive and negative solution.

Subtract 5 form both side so we get

x =  - 5± \sqrt{32}

The greater solution is when sqr root of 32 is positive so the answer to that is

\sqrt{32}  - 5 = 0.7

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