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Aleks04 [339]
2 years ago
15

Find the solutions to the equation 102x 11 = (x 6)2 – 2. Which values are approximate solutions to the equation? Select two answ

ers. –9. 6 –7. 4 –4. 6 –2. 4 0. 6.
Mathematics
1 answer:
otez555 [7]2 years ago
5 0

You can try finding the roots of the given quadratic equation to get to the solution of the equation.

There are two solutions to the given quadratic equation

x = 0.202, x = 113.798

<h3>How to find the roots of a quadratic equation?</h3>

Suppose that the given quadratic equation is ax^2 + bx  +c = 0

Then its roots are given as:

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

<h3>How to find the solution to the given equation?</h3>

First we will convert it in the aforesaid standard form.

102x + 11 = (x-6)^2 - 2\\102x + 11 + 2 = x^2 + 36 - 12x\\0  = x^2 -114x + 23\\x^2  -114x + 23 = 0\\

Thus, we have

a = 1. b = -114, c = 23

Using the formula for getting the roots of a quadratic equation,

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{114 \pm \sqrt{114^2 - 92}}{2} \\\\ x = 0.202 (\text{used "-" sign})\\\\x = 113.798 ( used "+" sign})

Thus, there are two solutions to the given quadratic equation

x = 0.202, x = 113.798

Learn more here about quadratic equations here:

brainly.com/question/3358603

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