Answer: the solutions to the equation 7x^2 = 15x + 9, rounded to the nearest tenth, are x ≈ 2.3 and x ≈ -0.8.
Step-by-step explanation: To solve the equation 7x^2 = 15x + 9, we can rearrange it into a quadratic equation by subtracting 15x and 9 from both sides:
7x^2 - 15x - 9 = 0
Now, we need to solve this quadratic equation. We can either factor it or use the quadratic formula. Let's use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 7, b = -15, and c = -9. Substituting these values into the formula, we have:
x = (-(-15) ± sqrt((-15)^2 - 4 * 7 * (-9))) / (2 * 7)
x = (15 ± sqrt(225 + 252)) / 14
x = (15 ± sqrt(477)) / 14
To the nearest tenth, we can evaluate the two solutions:
x ≈ (15 + sqrt(477)) / 14 ≈ 2.27 (rounded to the nearest tenth)
x ≈ (15 - sqrt(477)) / 14 ≈ -0.77 (rounded to the nearest tenth)
Therefore, the solutions to the equation 7x^2 = 15x + 9, rounded to the nearest tenth, are x ≈ 2.3 and x ≈ -0.8.