Please help it’s easy just im confused

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peachijmin

11.07.2021

Mathematics

$\boxed{x = 2 \pm \frac{ \sqrt{2} }{2} }$

Step-by-step explanation:

$Solve \: for \: x \: over \: the \: real \: numbers: \\ = 2 {x}^{2} - 8x = - 7 \\ \\ Divide \: both \: sides \: by \: 2: \\ = {x}^{2} -4x = - \frac{7}{2} \\ \\ Add \: 4 \: to \: both \: sides: \\ = {x}^{2} - 4x + 4 = \frac{1}{2} \\ \\ Write \: the \: left \: hand \: side \: as \: a \: square: \\ = {(x - 2)}^{2} = \frac{1}{2} \\ \\ Take \: the \: square \: root \: of \: both \: sides: \\ = x - 2 = \frac{1}{ \sqrt{2} } \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: x - 2 = - \frac{1}{ \sqrt{2} } \\ \\ Add \: 2 \: to \: both \: sides: \\ = x = 2 + \frac{1}{ \sqrt{2} } \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: x = 2 - \frac{1}{ \sqrt{2} } \\ \\ = x = 2 \pm \frac{1}{ \sqrt{2} } \\ \\ = x = 2 \pm (\frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }) \\ \\ = x = 2 \pm \frac{ \sqrt{2} }{2}$

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