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 6x^2 - 4x + 9x - 6 = 0 using the quadratic formula, first simplify the equation. Step 1: Combine like terms in the equation. 6x^2 + (-4x + 9x) - 6 = 0 6x^2 + 5x - 6 = 0 Step 2: Identify the coefficients a, b, and c from the standard quadratic form ax^2 + bx + c = 0. For 6x^2 + 5x - 6 = 0: a = 6 b = 5 c = -6 Step 3: Apply the quadratic formula. The quadratic formula is given by: x = -b ± sqrt(b^2 - 4ac)2a Step 4: Substitute the values of a, b, and c into the formula. x = -(5) ± sqrt((5)^2 - 4(6)(-6))2(6) Step 5: Simplify the expression under the square root (the discriminant). x = -5 ± sqrt(25 - (-144))12 x = -5 ± sqrt(25 + 144)12 x = -5 ± sqrt(169)12 Step 6: Calculate the square root and find the two solutions for x. Since sqrt(169) = 13: x = (-5 ± 13)/(12) This gives two possible solutions: x_1 = (-5 + 13)/(12) = (8)/(12) = (2)/(3) x_2 = (-5 - 13)/(12) = (-18)/(12) = -(3)/(2) The solutions are x = (2)/(3) and x = -(3)/(2). x = (2)/(3), x = -(3)/(2) Send me the next one 📸