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Simplifying 2x2 + 3x + 2 = 50 Reorder the terms: 2 + 3x + 2x2 = 50 Solving 2 + 3x + 2x2 = 50 Solving for variable 'x'. Reorder the terms: 2 + -50 + 3x + 2x2 = 50 + -50 Combine like terms: 2 + -50 = -48 -48 + 3x + 2x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -48 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + 1.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 1.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 1.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 1.5x + x2 = 0 + 24 1.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 1.5x + x2 = 24 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 = 24 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 24 + 0.5625 Combine like terms: 24 + 0.5625 = 24.5625 0.5625 + 1.5x + x2 = 24.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 24.5625 Calculate the square root of the right side: 4.9560569 Break this problem into two subproblems by setting (x + 0.75) equal to 4.9560569 and -4.9560569.Subproblem 1
x + 0.75 = 4.9560569 Simplifying x + 0.75 = 4.9560569 Reorder the terms: 0.75 + x = 4.9560569 Solving 0.75 + x = 4.9560569 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 = 4.9560569 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.9560569 + -0.75 x = 4.9560569 + -0.75 Combine like terms: 4.9560569 + -0.75 = 4.2060569 x = 4.2060569 Simplifying x = 4.2060569Subproblem 2
x + 0.75 = -4.9560569 Simplifying x + 0.75 = -4.9560569 Reorder the terms: 0.75 + x = -4.9560569 Solving 0.75 + x = -4.9560569 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 = -4.9560569 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.9560569 + -0.75 x = -4.9560569 + -0.75 Combine like terms: -4.9560569 + -0.75 = -5.7060569 x = -5.7060569 Simplifying x = -5.7060569Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2060569, -5.7060569}
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