Final answer:
To solve the quadratic equation 2x²-3x-7=0, use the Quadratic Formula by substituting a=2, b=-3, and c=-7 into the formula, which yields two solutions for x: x = (-3 ± √65) / 4.
Step-by-step explanation:
To solve the quadratic equation 2x²-3x-7=0 using the Quadratic Formula, first recognize the standard form ax² + bx + c = 0, where a, b, and c are coefficients. For this equation, a=2, b=-3, and c=-7. The Quadratic Formula states that the solutions for x are given by:
x = −(³√2) ± √(³√2)2 - 4(³√2)(³√7) / (2 ∙ ³√2)
Substitute the values of a, b, and c into the formula and simplify:
x = (−3 ± √(32 - 4 ∙ 2 ∙ (−7))) / (2 ∙ 2)
x = (−3 ± √(9 + 56)) / 4
x = (−3 ± √65) / 4
These are the two solutions for x using the Quadratic Formula. The roots of the quadratic equation are fractions and include square roots, which are irrational numbers.