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Simplifying 2x2 + -3x + 0 = 2916 Reorder the terms: 0 + -3x + 2x2 = 2916 Remove the zero: -3x + 2x2 = 2916 Solving -3x + 2x2 = 2916 Solving for variable 'x'. Reorder the terms: -2916 + -3x + 2x2 = 2916 + -2916 Combine like terms: 2916 + -2916 = 0 -2916 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1458 + -1.5x + x2 = 0 Move the constant term to the right: Add '1458' to each side of the equation. -1458 + -1.5x + 1458 + x2 = 0 + 1458 Reorder the terms: -1458 + 1458 + -1.5x + x2 = 0 + 1458 Combine like terms: -1458 + 1458 = 0 0 + -1.5x + x2 = 0 + 1458 -1.5x + x2 = 0 + 1458 Combine like terms: 0 + 1458 = 1458 -1.5x + x2 = 1458 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 1458 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 1458 + 0.5625 Combine like terms: 1458 + 0.5625 = 1458.5625 0.5625 + -1.5x + x2 = 1458.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1458.5625 Calculate the square root of the right side: 38.191131169 Break this problem into two subproblems by setting (x + -0.75) equal to 38.191131169 and -38.191131169.Subproblem 1
x + -0.75 = 38.191131169 Simplifying x + -0.75 = 38.191131169 Reorder the terms: -0.75 + x = 38.191131169 Solving -0.75 + x = 38.191131169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 38.191131169 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 38.191131169 + 0.75 x = 38.191131169 + 0.75 Combine like terms: 38.191131169 + 0.75 = 38.941131169 x = 38.941131169 Simplifying x = 38.941131169Subproblem 2
x + -0.75 = -38.191131169 Simplifying x + -0.75 = -38.191131169 Reorder the terms: -0.75 + x = -38.191131169 Solving -0.75 + x = -38.191131169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -38.191131169 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -38.191131169 + 0.75 x = -38.191131169 + 0.75 Combine like terms: -38.191131169 + 0.75 = -37.441131169 x = -37.441131169 Simplifying x = -37.441131169Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.941131169, -37.441131169}
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