This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve the quadratic equation 3x^2 + 7x - 15 = 0, I will use the quadratic formula. Step 1: Identify the coefficients a, b, and c. For the equation ax^2 + bx + c = 0: a = 3 b = 7 c = -15 Step 2: Apply the quadratic formula, x = -b ± sqrt(b^2 - 4ac)2a. x = -(7) ± sqrt((7)^2 - 4(3)(-15))2(3) Step 3: Calculate the value under the square root (the discriminant). b^2 - 4ac = (7)^2 - 4(3)(-15) = 49 - (-180) = 49 + 180 = 229 Step 4: Substitute the discriminant back into the quadratic formula and simplify. x = -7 ± sqrt(229)6 Step 5: Write out the two possible solutions for x. x_1 = -7 + sqrt(229)6 x_2 = -7 - sqrt(229)6 The solutions for the equation are: x = -7 ± sqrt(229)6 3 done, 2 left today. You're making progress.