Question

solve for x using the quadratic formula.use solution history$2x^2 - 7x - 7 = 0$choose an action to perform.ways to rewrite expressionsapply exponentdistributefactor greatest factorperform multiplicationrewrite signscombine like termseliminate radicalfactor quadraticrewrite fractionsequation transformationsadd to both sidessubtract from both sidesmultiply both sidesdivide both sidesapply quadratic formulaother actionsapply zero product propertyseparate roots

Explanation:

Step1: Identify quadratic coefficients

For $2x^2 -7x -7=0$, $a=2$, $b=-7$, $c=-7$

Step2: Recall quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Substitute values into formula

$$x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(-7)}}{2(2)}$$

Step4: Calculate discriminant

$\sqrt{49 + 56}=\sqrt{105}$

Step5: Simplify the expression

$$x=\frac{7\pm\sqrt{105}}{4}$$

Answer:

$x=\frac{7+\sqrt{105}}{4}$ and $x=\frac{7-\sqrt{105}}{4}$