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Simplifying 2x2 + -3x + -400 = 0 Reorder the terms: -400 + -3x + 2x2 = 0 Solving -400 + -3x + 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'. -200 + -1.5x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -1.5x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -1.5x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -1.5x + x2 = 0 + 200 -1.5x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -1.5x + x2 = 200 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 = 200 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 200 + 0.5625 Combine like terms: 200 + 0.5625 = 200.5625 0.5625 + -1.5x + x2 = 200.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 200.5625 Calculate the square root of the right side: 14.162009038 Break this problem into two subproblems by setting (x + -0.75) equal to 14.162009038 and -14.162009038.Subproblem 1
x + -0.75 = 14.162009038 Simplifying x + -0.75 = 14.162009038 Reorder the terms: -0.75 + x = 14.162009038 Solving -0.75 + x = 14.162009038 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 = 14.162009038 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 14.162009038 + 0.75 x = 14.162009038 + 0.75 Combine like terms: 14.162009038 + 0.75 = 14.912009038 x = 14.912009038 Simplifying x = 14.912009038Subproblem 2
x + -0.75 = -14.162009038 Simplifying x + -0.75 = -14.162009038 Reorder the terms: -0.75 + x = -14.162009038 Solving -0.75 + x = -14.162009038 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 = -14.162009038 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -14.162009038 + 0.75 x = -14.162009038 + 0.75 Combine like terms: -14.162009038 + 0.75 = -13.412009038 x = -13.412009038 Simplifying x = -13.412009038Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.912009038, -13.412009038}
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