Rozwiąż równanie kwadratowe ( krok po kroku bez żadnych skrótów). ( np. x^2 - znaczy x do kwadratu, (x-1)- oznacza nawias do kwadratu) x^2+6x+9= 2(x-1)^2

x²+6x+9=2(x²-2x+1) 2x²-4x+2=x²+6x+9 2x²-4x+2-x²-6x-9=0 x²-10x-7=0 Δ=b²-4ac Δ=10²+4*7=128 √Δ=8√2 x=1/2*(10-8√2)=5-4√2  v  x=5+4√2

[latex]x^{2}+6x+9 = 2(x-1)^{2}\\x^{2}+6x+9 = 2(x^{2}-2x+1)\\x^{2}+6x+9 = 2x^{2}-4x+2\\x^{2}-2x^{2}+6x+4x+9-2 = 0\\-x^{2}+10x+7 = 0 |*(-1)\\x^{2}-10x-7 = 0\\a = 1, b = -10, c = -7[/latex] [latex]Delta} = b^{2}-4ac = (-10)^{2}-4*1*(-7) = 100+28 = 128\\sqrt{Delta} = sqrt{128} = sqrt{64*2} = 8sqrt{2}\\x_1 = frac{-b-sqrt{Delta}}{2a} = frac{-(-10)-8sqrt{2}}{2} = frac{10-8sqrt{2}}{2} = 5-4sqrt{2}\\x_2 = frac{-b+sqrt{Delta}}{2a} = frac{10+8sqrt{2}}{2} = 5+4sqrt{2}[/latex]