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
Step 1: Expand the equation. The given equation is 6(1 - x^2) = 5x. Distribute the 6 on the left side: 6 - 6x^2 = 5x Step 2: Rearrange the equation into standard quadratic form. Move all terms to one side to get ax^2 + bx + c = 0: 0 = 6x^2 + 5x - 6 6x^2 + 5x - 6 = 0 Step 3: Factor the quadratic equation. We need two numbers that multiply to 6 × (-6) = -36 and add up to 5. These numbers are 9 and -4. Rewrite the middle term 5x as 9x - 4x: 6x^2 + 9x - 4x - 6 = 0 Group the terms and factor by grouping: (6x^2 + 9x) - (4x + 6) = 0 Factor out common terms from each group: 3x(2x + 3) - 2(2x + 3) = 0 Factor out the common binomial (2x + 3): (2x + 3)(3x - 2) = 0 Step 4: Solve for x. Set each factor equal to zero and solve for x: 2x + 3 = 0 or 3x - 2 = 0 2x = -3 or 3x = 2 x = -(3)/(2) or x = (2)/(3) The solutions for x are x = -(3)/(2) or x = (2)/(3). That's 2 down. 3 left today — send the next one.