Find all values of x satisfying the given conditions. y1 = 2x2 + 5x - 4, y2 = - x2 + 15x - 10, and y1 - y2 = 0

Ch. 1 - Equations and Inequalities

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Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 121

Capitolo 2, Problema 121

Find all values of x satisfying the given conditions. y₁ = 2x² + 5x - 4, y₂ = - x² + 15x - 10, and y₁ - y₂ = 0

Guida verificata passo dopo passo

Step 1: Start by substituting the given expressions for y1 and y2 into the equation y1 - y2 = 0. This gives (2x^2 + 5x - 4) - (-x^2 + 15x - 10) = 0.

Step 2: Simplify the equation by distributing the negative sign across the terms in y2. This results in 2x^2 + 5x - 4 + x^2 - 15x + 10 = 0.

Step 3: Combine like terms. Group the x^2 terms, the x terms, and the constant terms together. This simplifies to 3x^2 - 10x + 6 = 0.

Step 4: Factorize the quadratic equation 3x^2 - 10x + 6 = 0, if possible. Alternatively, use the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, where a = 3, b = -10, and c = 6.

Step 5: Solve for the two possible values of x by substituting the values of a, b, and c into the quadratic formula or by solving the factored form of the equation. These values of x are the solutions to the problem.

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