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Simplifying 3.5x + 2x2 = 1 Solving 3.5x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 3.5x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 3.5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.75x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.75x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.75x + x2 = 0 + 0.5 1.75x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.75x + x2 = 0.5 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 0.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 0.5 + 0.765625 Combine like terms: 0.5 + 0.765625 = 1.265625 0.765625 + 1.75x + x2 = 1.265625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 1.265625 Calculate the square root of the right side: 1.125 Break this problem into two subproblems by setting (x + 0.875) equal to 1.125 and -1.125.Subproblem 1
x + 0.875 = 1.125 Simplifying x + 0.875 = 1.125 Reorder the terms: 0.875 + x = 1.125 Solving 0.875 + x = 1.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.125 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.125 + -0.875 x = 1.125 + -0.875 Combine like terms: 1.125 + -0.875 = 0.25 x = 0.25 Simplifying x = 0.25Subproblem 2
x + 0.875 = -1.125 Simplifying x + 0.875 = -1.125 Reorder the terms: 0.875 + x = -1.125 Solving 0.875 + x = -1.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.125 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.125 + -0.875 x = -1.125 + -0.875 Combine like terms: -1.125 + -0.875 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25, -2}
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