Answer: 0.444
Step-by-step explanation:
1.5 - 1.056 = 0.444
Answer:
![x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B3%2B%20%5Csqrt%7B29%7D%7D%7B2%7D%2C%20%5Cquad%20%5Cdfrac%7B3-%20%5Csqrt%7B29%7D%7D%7B2%7D)
Step-by-step explanation:
<u>Quadratic Formula</u>
![x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5Cquad%5Ctextsf%7Bwhen%20%7D%5C%3Aax%5E2%2Bbx%2Bc%3D0)
<u>Given quadratic equation</u>:
![x^2-3x-5=0](https://tex.z-dn.net/?f=x%5E2-3x-5%3D0)
<u>Define the variables</u>:
![\implies a=1, \quad b=-3, \quad c=-5](https://tex.z-dn.net/?f=%5Cimplies%20a%3D1%2C%20%5Cquad%20b%3D-3%2C%20%5Cquad%20c%3D-5)
<u>Substitute</u> the defined variables into the quadratic formula and <u>solve for x</u>:
![\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)}}{2(1)}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D%5Cdfrac%7B-%28-3%29%20%5Cpm%20%5Csqrt%7B%28-3%29%5E2-4%281%29%28-5%29%7D%7D%7B2%281%29%7D)
![\implies x=\dfrac{3 \pm \sqrt{9+20}}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D%5Cdfrac%7B3%20%5Cpm%20%5Csqrt%7B9%2B20%7D%7D%7B2%7D)
![\implies x=\dfrac{3 \pm \sqrt{29}}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D%5Cdfrac%7B3%20%5Cpm%20%5Csqrt%7B29%7D%7D%7B2%7D)
Therefore, the exact solutions to the given <u>quadratic equation</u> are:
![x=\dfrac{3+ \sqrt{29}}{2}, \quad \dfrac{3- \sqrt{29}}{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B3%2B%20%5Csqrt%7B29%7D%7D%7B2%7D%2C%20%5Cquad%20%5Cdfrac%7B3-%20%5Csqrt%7B29%7D%7D%7B2%7D)
Learn more about the quadratic formula here:
brainly.com/question/27868610
brainly.com/question/27750885
The range of values of x as shown in the diagram is -9 < x < 15
<h3>Inequality expressions</h3>
Inequality are expressions not separated by an equal sign. The required inequality expression is given as:
|9x - 27| < 108
For the positive inequality
9x - 27 < 108
9x < 108 +27
9x < 135
x < 15
For the negative inequality
-9x + 27 < 108
-9x < 108 - 27
-9x < 91
x > -9
-9 < x
Hence the range of values of x as shown in the diagram is -9 < x < 15
Learn more on inequality here: brainly.com/question/24372553
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