11:08 20 Spiral Review \#5 Assignment Overview $$ 2 \approx $$ DeltaMath Score: 0/2 Penalty: none Quadratic Formula Decimal Answer Question Video Examples Solve the equation $$ 4 x^{2}+15 x+17=3 x^{2} $$ to the nearest tenth. Answer Attempt 2 out of 2 Additional Solution No Solution $$ x= $$ $$ \square $$ Submit Answer Still Stuck?

Question

UpStudy AI · Accepted Answer

1. Rewrite the equation:
   $$
   4x^2 + 15x + 17 = 3x^2
   $$
   Subtract $$3x^2$$ from both sides to obtain:
   $$
   4x^2 - 3x^2 + 15x + 17 = 0 \quad \Longrightarrow \quad x^2 + 15x + 17 = 0
   $$

2. Identify the coefficients of the quadratic equation $$ax^2+bx+c=0$$:
   $$
   a = 1,\quad b = 15,\quad c = 17
   $$

3. Apply the quadratic formula:
   $$
   x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
   $$
   Substitute the values:
   $$
   x = \frac{-15 \pm \sqrt{15^2 - 4(1)(17)}}{2(1)} = \frac{-15 \pm \sqrt{225 - 68}}{2} = \frac{-15 \pm \sqrt{157}}{2}
   $$

4. Evaluate the square root and approximate the solutions:
   $$
   \sqrt{157} \approx 12.53
   $$
   Thus, the solutions are approximately:
   $$
   x \approx \frac{-15 + 12.53}{2} \quad \text{and} \quad x \approx \frac{-15 - 12.53}{2}
   $$
   
   Calculate each:
   $$
   x \approx \frac{-2.47}{2} \approx -1.2 \quad \text{and} \quad x \approx \frac{-27.53}{2} \approx -13.8
   $$

5. Therefore, the solutions to the equation, rounded to the nearest tenth, are:
   $$
   x \approx -1.2 \quad \text{or} \quad x \approx -13.8
   $$
The solutions are $$ x \approx -1.2 $$ and $$ x \approx -13.8 $$.

11:08
20
Spiral Review #5
Assignment Overview
DeltaMath
Score: 0/2
Penalty: none

Quadratic Formula Decimal Answer

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11:08 20 Spiral Review #5 Assignment Overview DeltaMath Score: 0/2 Penalty: none Quadratic Formula Decimal Answer Question Video Examples Solve the equation to the nearest tenth. Answer Attempt 2 out of 2 Additional Solution No Solution Submit Answer Still Stuck?