Identify the 35th term of an arithmetic sequence where a1 = −7 and a18 = 95.
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The mistake is in Step 1. The solver should have also squared when squaring the other side of the equation.
Complete the square for x and y.
7x^2 + 3y^2 - 28x - 12y = -19
7x^2 - 28x + 3y^2 - 12y = -19
7(x^2 - 4x) + 3(y^2 - 4y) = -19
7(x^2 - 4x + 4) + 3(y^2 - 4y + 4) = -19 + 28 + 12
7(x - 2)^2 + 3(y - 2)^2 = 21
7x^2 + 3y^2 - 28x - 12y = -19
7x^2 - 28x + 3y^2 - 12y = -19
7(x^2 - 4x) + 3(y^2 - 4y) = -19
7(x^2 - 4x + 4) + 3(y^2 - 4y + 4) = -19 + 28 + 12
7(x - 2)^2 + 3(y - 2)^2 = 21