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Simplifying 2x2 + 3x = 1400 Reorder the terms: 3x + 2x2 = 1400 Solving 3x + 2x2 = 1400 Solving for variable 'x'. Reorder the terms: -1400 + 3x + 2x2 = 1400 + -1400 Combine like terms: 1400 + -1400 = 0 -1400 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -700 + 1.5x + x2 = 0 Move the constant term to the right: Add '700' to each side of the equation. -700 + 1.5x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + 1.5x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + 1.5x + x2 = 0 + 700 1.5x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 1.5x + x2 = 700 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 = 700 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 700 + 0.5625 Combine like terms: 700 + 0.5625 = 700.5625 0.5625 + 1.5x + x2 = 700.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 700.5625 Calculate the square root of the right side: 26.468141227 Break this problem into two subproblems by setting (x + 0.75) equal to 26.468141227 and -26.468141227.Subproblem 1
x + 0.75 = 26.468141227 Simplifying x + 0.75 = 26.468141227 Reorder the terms: 0.75 + x = 26.468141227 Solving 0.75 + x = 26.468141227 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 = 26.468141227 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 26.468141227 + -0.75 x = 26.468141227 + -0.75 Combine like terms: 26.468141227 + -0.75 = 25.718141227 x = 25.718141227 Simplifying x = 25.718141227Subproblem 2
x + 0.75 = -26.468141227 Simplifying x + 0.75 = -26.468141227 Reorder the terms: 0.75 + x = -26.468141227 Solving 0.75 + x = -26.468141227 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 = -26.468141227 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -26.468141227 + -0.75 x = -26.468141227 + -0.75 Combine like terms: -26.468141227 + -0.75 = -27.218141227 x = -27.218141227 Simplifying x = -27.218141227Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.718141227, -27.218141227}
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