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Solve the equation 5x^(2)+15 x-2=0 to the nearest tenth. Answer: x=

Solve the equation 5x2+15x−2=0 5 x^{2}+15 x-2=0 to the nearest tenth.\newlineAnswer: x= x=

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Q. Solve the equation 5x2+15x−2=0 5 x^{2}+15 x-2=0 to the nearest tenth.\newlineAnswer: x= x=
  1. Identify Equation Type: Identify the type of equation.\newlineWe have a quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0, where a=5a = 5, b=15b = 15, and c=−2c = -2.
  2. Apply Quadratic Formula: Apply the quadratic formula.\newlineThe quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. We will use this to find the values of xx.
  3. Substitute Values: Substitute the values of aa, bb, and cc into the quadratic formula.x=−(15)±(15)2−4(5)(−2)2(5)x = \frac{{-(15) \pm \sqrt{{(15)^2 - 4(5)(-2)}}}}{{2(5)}}
  4. Simplify Under Square Root: Simplify under the square root.\newlinex=−15±225+4010x = \frac{{-15 \pm \sqrt{{225 + 40}}}}{10}\newlinex=−15±26510x = \frac{{-15 \pm \sqrt{265}}}{10}
  5. Calculate Discriminant: Calculate the discriminant (265\sqrt{265}) and simplify the equation further.\newlinex=−15±26510x = \frac{-15 \pm \sqrt{265}}{10}
  6. Find Possible Values: Find the two possible values for xx.x1=−15+26510x_1 = \frac{{-15 + \sqrt{265}}}{{10}}x2=−15−26510x_2 = \frac{{-15 - \sqrt{265}}}{{10}}
  7. Calculate Numerical Values: Calculate the numerical values for x1x_1 and x2x_2.
    x1≈(−15+16.279)/10x_1 \approx (-15 + 16.279) / 10
    x1≈1.279/10x_1 \approx 1.279 / 10
    x1≈0.128x_1 \approx 0.128

    x2≈(−15−16.279)/10x_2 \approx (-15 - 16.279) / 10
    x2≈−31.279/10x_2 \approx -31.279 / 10
    x2≈−3.128x_2 \approx -3.128
  8. Round Solutions: Round the solutions to the nearest tenth. \newlinex1≈0.1x_1 \approx 0.1\newlinex2≈−3.1x_2 \approx -3.1

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