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Simplifying 2x2 + -6.5x + -42 = 0 Reorder the terms: -42 + -6.5x + 2x2 = 0 Solving -42 + -6.5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + -3.25x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -3.25x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -3.25x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -3.25x + x2 = 0 + 21 -3.25x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -3.25x + x2 = 21 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 21 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 21 + 2.640625 Combine like terms: 21 + 2.640625 = 23.640625 2.640625 + -3.25x + x2 = 23.640625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 23.640625 Calculate the square root of the right side: 4.862162585 Break this problem into two subproblems by setting (x + -1.625) equal to 4.862162585 and -4.862162585.Subproblem 1
x + -1.625 = 4.862162585 Simplifying x + -1.625 = 4.862162585 Reorder the terms: -1.625 + x = 4.862162585 Solving -1.625 + x = 4.862162585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 4.862162585 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 4.862162585 + 1.625 x = 4.862162585 + 1.625 Combine like terms: 4.862162585 + 1.625 = 6.487162585 x = 6.487162585 Simplifying x = 6.487162585Subproblem 2
x + -1.625 = -4.862162585 Simplifying x + -1.625 = -4.862162585 Reorder the terms: -1.625 + x = -4.862162585 Solving -1.625 + x = -4.862162585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -4.862162585 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -4.862162585 + 1.625 x = -4.862162585 + 1.625 Combine like terms: -4.862162585 + 1.625 = -3.237162585 x = -3.237162585 Simplifying x = -3.237162585Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.487162585, -3.237162585}
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