Question

Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?

Answer 1

`x=2+√(11),\:x=2-√(11)`

Explanation:

`x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_(1,\:2)=(-\left(-4\right)\pm √(\left(-4\right)^2-4\cdot \:1\left(-7\right)))/(2\cdot \:1)\\x=(-\left(-4\right)+√(\left(-4\right)^2-4\cdot \:1\left(-7\right)))/(2\cdot \:1):\quad 2+√(11)`

`x=(-\left(-4\right)-√(\left(-4\right)^2-4\cdot \:1\left(-7\right)))/(2\cdot \:1):\quad 2-√(11)\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+√(11),\:x=2-√(11)`