using the quadratic formula to solve \( 2x^2 = 4x – 7 \), what are the values of x?
Equation \( 2x^2 = 4x – 7 \to 2x^2 -4x + 7 =0 \) [Convert in Quadratic Equation to find the value of x]
\( 2x^2 + (-4)x + 7 =0 \)
where a= 2, b= -4 and c=7
The Quadratic Equation formula is \(x = {-b \pm \sqrt{b^2-4ac} \over 2a} \)
=> \(x = {-(-4) \pm \sqrt{(-4)^2- 4 \times 2 \times 7} \over 2 \times 2} \)
=> \(x = {4 \pm \sqrt{16- 56} \over 4} \)
=> \(x = {4 \pm \sqrt{-40} \over 4} \)
=> \(x = { \frac{4}{4} \pm \sqrt{-40 \over 16} } \)
=> \(x = { 1 \pm \sqrt{-10 \over 4 } } \)
=> \(x = { 1 \pm \frac{\sqrt{-10}}{2} } \) [The value of \( \sqrt{-10} = 3.16i \)]
=> \(x = { 1 \pm \frac{3.16i}{2} } \)
=> \(x = { 1 \pm 1.58 i } \)
=> \(x = 1 + 1.58 i \to 1 – 1.58 i \)