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Simplifying 2x2 + 7x = 32 Reorder the terms: 7x + 2x2 = 32 Solving 7x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 7x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16 + 3.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 3.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 3.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 3.5x + x2 = 0 + 16 3.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 3.5x + x2 = 16 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 16 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 16 + 3.0625 Combine like terms: 16 + 3.0625 = 19.0625 3.0625 + 3.5x + x2 = 19.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (x + 1.75) equal to 4.366062299 and -4.366062299.Subproblem 1
x + 1.75 = 4.366062299 Simplifying x + 1.75 = 4.366062299 Reorder the terms: 1.75 + x = 4.366062299 Solving 1.75 + x = 4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.366062299 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.366062299 + -1.75 x = 4.366062299 + -1.75 Combine like terms: 4.366062299 + -1.75 = 2.616062299 x = 2.616062299 Simplifying x = 2.616062299Subproblem 2
x + 1.75 = -4.366062299 Simplifying x + 1.75 = -4.366062299 Reorder the terms: 1.75 + x = -4.366062299 Solving 1.75 + x = -4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.366062299 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.366062299 + -1.75 x = -4.366062299 + -1.75 Combine like terms: -4.366062299 + -1.75 = -6.116062299 x = -6.116062299 Simplifying x = -6.116062299Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.616062299, -6.116062299}
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