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Simplifying 2x2 + 3x = 103 Reorder the terms: 3x + 2x2 = 103 Solving 3x + 2x2 = 103 Solving for variable 'x'. Reorder the terms: -103 + 3x + 2x2 = 103 + -103 Combine like terms: 103 + -103 = 0 -103 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -51.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '51.5' to each side of the equation. -51.5 + 1.5x + 51.5 + x2 = 0 + 51.5 Reorder the terms: -51.5 + 51.5 + 1.5x + x2 = 0 + 51.5 Combine like terms: -51.5 + 51.5 = 0.0 0.0 + 1.5x + x2 = 0 + 51.5 1.5x + x2 = 0 + 51.5 Combine like terms: 0 + 51.5 = 51.5 1.5x + x2 = 51.5 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 = 51.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 51.5 + 0.5625 Combine like terms: 51.5 + 0.5625 = 52.0625 0.5625 + 1.5x + x2 = 52.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 52.0625 Calculate the square root of the right side: 7.215434845 Break this problem into two subproblems by setting (x + 0.75) equal to 7.215434845 and -7.215434845.Subproblem 1
x + 0.75 = 7.215434845 Simplifying x + 0.75 = 7.215434845 Reorder the terms: 0.75 + x = 7.215434845 Solving 0.75 + x = 7.215434845 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 = 7.215434845 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.215434845 + -0.75 x = 7.215434845 + -0.75 Combine like terms: 7.215434845 + -0.75 = 6.465434845 x = 6.465434845 Simplifying x = 6.465434845Subproblem 2
x + 0.75 = -7.215434845 Simplifying x + 0.75 = -7.215434845 Reorder the terms: 0.75 + x = -7.215434845 Solving 0.75 + x = -7.215434845 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 = -7.215434845 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.215434845 + -0.75 x = -7.215434845 + -0.75 Combine like terms: -7.215434845 + -0.75 = -7.965434845 x = -7.965434845 Simplifying x = -7.965434845Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.465434845, -7.965434845}
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