Question

Which method is best to use to solve the equation 4x^2– 29 = 0?

Answer 1

$\huge\text{Hey there!}$

$\mathsf{4x^2 - 29 = 0}\\\\\large\textsf{ADD 29 to BOTH SIDES}\\\mathsf{4x^2 - 29 + 29 = 0 + 29}\\\\\textsf{CANCEL out: -29 + 29 because that gives you 0}\\\\\textsf{KEEP: 0 + 29 because that helps you solve for the x-value}\\\\\mathsf{0 + 29 = \bf 29}\\\\\textsf{NEW EQUATION: }\mathsf{4x^2 = 29}\\\\\large\textsf{DIVIDE 4 to BOTH SIDES}\mathsf{\dfrac{4x^2}{4}=\dfrac{29}{4}}\\\\\large\textsf{{CANCEL out:} }\mathsf{\dfrac{4}{4}}\textsf{ because that gives you 0}$

$\textsf{KEEP: }\mathsf{\dfrac{29}{9}}\large\textsf{ because that helps solve for the x-value}$

$\textsf{NEW EQUATION: }\mathsf{x^2=\dfrac{29}{4}}$

$\large\textsf{TAKE the SQUARE ROOT}$

$\mathsf{x = \pm \sqrt{\dfrac{29}{4}}}$

$\text{Random fact: if you see the symbol }\mathsf{\bf \pm}\text{ it usually means plus-or-minus.}\\\\\text{Okay, now lets answer the last step to your question!}$

$\mathsf{\sqrt{\dfrac{29}{4}}= \boxed{\bf 2.692582}}}\\\\\mathsf{OR}\\\mathsf{- \sqrt{\dfrac{29}{4}} =\boxed{ \bf -2.692582}}$

$\boxed{\boxed{\huge\textsf{Answer: \bf x = 2.692582 or x = -2.692582 }}}\\\huge\checkmark$

$\large\text{Good luck on your assignment and enjoy your day!}$

~$\frak{Amphitrite1040:)}$