Open Question
In Exercises 115–122, find all values of x satisfying the given conditions.y1 = 2x^2 + 5x - 4, y2 = - x^2 + 15x - 10, and y1 - y2 = 0
1. Equations & Inequalities
The Quadratic Formula
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Solve the given quadratic equation using the quadratic formula.
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Verified step by step guidance1
Start by rewriting the quadratic equation in standard form: \(2x^2 - 3x + 3 = 0\).
Identify the coefficients \(a\), \(b\), and \(c\) from the equation \(ax^2 + bx + c = 0\). Here, \(a = 2\), \(b = -3\), and \(c = 3\).
Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Substitute the values of \(a\), \(b\), and \(c\) into the formula.
Calculate the discriminant \(b^2 - 4ac\). Substitute \(b = -3\), \(a = 2\), and \(c = 3\) to find \((-3)^2 - 4(2)(3)\).
Since the discriminant is negative, the solutions will involve imaginary numbers. Simplify the expression under the square root and solve for \(x\) using the quadratic formula.
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