5. Resolver las siguientes ecuaciones de Segundo grado por completacion del trinomiocuadrado perfecto :0 = x² - 13x - 30?

Respuesta : Explicación paso a paso : <img src="https://tex.z-dn.net/?f=%5Ctexttt%7BLa%20ecuaci%5C%27on%20es%3A%7D%5C%5C%5C%5Cx%5E%7B2%7D-13x%2B30%3D0%5C%5C%5Ctextbf%7BEst%C3%A1%20ecuaci%5C%27on%20podemos%20factorizar%20la%7D%5C%5C%5Ctexttt%7Bpor%20simple%20inspecci%5C%27on%2Cbuscando%20dos%20n%5C%27umeros%7D%5C%5C%5Ctexttt%7Bque%20multiplicados%20nos%20den%2030%20y%20sumados%20nos%20den%20-13%7D%5C%5C%5Ctexttt%7Bdichos%20n%5C%27umeros%20son%20-3%20y%20-10%20porque%3A%7D%5C%2C%5C%2C%28-3%29%28-10%29%3D30%5C%2C%5C%2C%5Ctexttt%7By%7D%5C%2C%5C%2C-3-10%3D-13%5C%5C%5Ctexttt%7BPor%20lo%20tanto%3A%7D%5C%5C%5C%5Cx%5E%7B2%7D-13x%2B30%3D0%5C%5C%28x-3%29%28x-10%29%3D0%5C%5C%5Ctexttt%7BAs%5C%27i%20las%20ra%5C%27ices%20son%3A%7D%5C%5C%5C%5Cx_%7B1%7D%3D3%5C%5Cx_%7B2%7D%3D10" /><img src="https://tex.z-dn.net/?f=%5Ctexttt%7BLa%20otra%20opci%5C%27on%20es%20factorizar%20la%20ecuaci%5C%27on%20usando%7D%5C%5C%5Ctexttt%7Bel%20m%5C%27etodo%20de%20completar%20el%20cuadrado%20entonces%3A%7D%5C%5C%5C%5Cx%5E%7B2%7D-13x%2B30%3D0%5C%5C%5Ctexttt%7BTransponemos%20el%20t%5C%27ermino%20constante%3A%7D%5C%5Cx%5E%7B2%7D-13x%3D-30%5C%5C%5Ctexttt%7BSumamos%20el%20cuadrado%20de%20la%20mitad%7D%5C%5C%5Ctexttt%7Bdel%20segundo%20t%5C%27ermino%20a%20ambos%20lados%20de%20la%20ecuaci%5C%27on%7D%5C%5Cx%5E%7B2%7D-13x%2B%28%5Cfrac%7B13%7D%7B2%7D%29%5E%7B2%7D%3D-30%2B%28%5Cfrac%7B13%7D%7B2%7D%29%5E%7B2%7D%5C%5C%5Ctexttt%7BDesarrollamos%3A%7D%5C%5Cx%5E%7B2%7D-13x%2B%5Cfrac%7B169%7D%7B4%7D%3D-30%2B%5Cfrac%7B169%7D%7B4%7D%5C%5C%5Ctextbf%7BFactorizamos%20el%20primer%20miembro%20y%20simplificamos%7D%5C%5C%5Ctexttt%7Bel%20segundo%3A%7D%5C%5C%28x-%5Cfrac%7B13%7D%7B2%7D%29%5E%7B2%7D%3D%5Cfrac%7B49%7D%7B4%7D%5C%5C%5Ctexttt%7BAs%5C%27i%20la%20ecuaci%5C%27on%20factorizada%20es%3A%7D%5C%5Cx%5E%7B2%7D-13x%2B30%3D%28x-%5Cfrac%7B13%7D%7B2%7D%29%5E%7B2%7D-%5Cfrac%7B49%7D%7B4%7D%3D0%5C%5C%5Ctexttt%7BEst%C3%A1%20forma%20es%20una%20diferencia%20de%20cuadrados%2C%20es%20decir%3A%7D%5C%5C%5C%5Ca%5E%7B2%7D-b%5E%7B2%7D%3D%28a-b%29%28%28a%2Bb%29%5C%5C%5Ctexttt%7Bpor%20tanto%20haciendo%20a%3D%28x-13%2F2%29%20y%20b%3D7%2F2%20obtenemos%3A%7D%5C%5C%5C%5C%28x-%5Cfrac%7B13%7D%7B2%7D%29%5E%7B2%7D-%5Cfrac%7B49%7D%7B4%7D%3D%28%28x-%5Cfrac%7B13%7D%7B2%7D%29-%5Cfrac%7B7%7D%7B2%7D%29%28%28x-%5Cfrac%7B13%7D%7B2%7D%29%2B%5Cfrac%7B7%7D%7B2%7D%29%3D0%5C%5C%5Ctextbf%7BLas%20ra%5C%27ices%20son%3A%7D%5C%5C%5C%5Cx_%7B1%7D%3D%5Cfrac%7B13%7D%7B2%7D%2B%5Cfrac%7B7%7D%7B2%7D%3D%5Cfrac%7B20%7D%7B2%7D%3D10%5C%5Cx_%7B2%7D%3D%5Cfrac%7B13%7D%7B2%7D-%5Cfrac%7B7%7D%7B2%7D%3D%5Cfrac%7B6%7D%7B2%7D%3D3" />.