find the value of x using abc formula 1.x²+x-6=0 2.x²-14x+c 3.x²+5x=-6 4.2x²=50​

Answer:The "abc formula" you're referring to is the quadratic formula, which is used to find the solutions (roots) of a quadratic equation in the form ax² + bx + c = 0. The formula is:x = (-b ± √(b² - 4ac)) / (2a)Let's apply this to each equation:1. x² + x - 6 = 0a = 1, b = 1, c = -6x = (-1 ± √(1² - 4 * 1 * -6)) / (2 * 1)x = (-1 ± √(1 + 24)) / 2x = (-1 ± √25) / 2x = (-1 ± 5) / 2x₁ = (-1 + 5) / 2 = 4 / 2 = 2x₂ = (-1 - 5) / 2 = -6 / 2 = -3Solutions: x = 2, x = -32. x² - 14x + cThis isn't an equation; it's an expression because it's not set equal to anything. We can't solve for 'x' without knowing the value of 'c' or what the expression is equal to. If you meant to solve for 'c' given certain roots, please provide that information.3. x² + 5x = -6First, rewrite the equation in the standard form: x² + 5x + 6 = 0a = 1, b = 5, c = 6x = (-5 ± √(5² - 4 * 1 * 6)) / (2 * 1)x = (-5 ± √(25 - 24)) / 2x = (-5 ± √1) / 2x = (-5 ± 1) / 2x₁ = (-5 + 1) / 2 = -4 / 2 = -2x₂ = (-5 - 1) / 2 = -6 / 2 = -3Solutions: x = -2, x = -34. 2x² = 50First, rewrite the equation in the standard form: 2x² - 50 = 0a = 2, b = 0, c = -50x = (0 ± √(0² - 4 * 2 * -50)) / (2 * 2)x = (0 ± √(0 + 400)) / 4x = (0 ± √400) / 4x = (0 ± 20) / 4x₁ = (0 + 20) / 4 = 20 / 4 = 5x₂ = (0 - 20) / 4 = -20 / 4 = -5Solutions: x = 5, x = -5Alternatively, you could solve equation 4 like this:2x² = 50x² = 25x = ±√25x = ±5This method is simpler when 'b' is 0.Summary of Solutions:x = 2, x = -3Cannot be solved without more information.x = -2, x = -3x = 5, x = -5

Answered by Velvrix | 2025-08-19