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Simplifying x2 + 3.5x + 3.0625 = 0 Reorder the terms: 3.0625 + 3.5x + x2 = 0 Solving 3.0625 + 3.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3.0625' to each side of the equation. 3.0625 + 3.5x + -3.0625 + x2 = 0 + -3.0625 Reorder the terms: 3.0625 + -3.0625 + 3.5x + x2 = 0 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 0.0000 + 3.5x + x2 = 0 + -3.0625 3.5x + x2 = 0 + -3.0625 Combine like terms: 0 + -3.0625 = -3.0625 3.5x + x2 = -3.0625 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 = -3.0625 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -3.0625 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 3.0625 + 3.5x + x2 = 0.0000 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + 1.75) equal to 0.0000 and 0.0000.Subproblem 1
x + 1.75 = 0.0000 Simplifying x + 1.75 = 0.0000 Reorder the terms: 1.75 + x = 0.0000 Solving 1.75 + x = 0.0000 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 = 0.0000 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 0.0000 + -1.75 x = 0.0000 + -1.75 Combine like terms: 0.0000 + -1.75 = -1.75 x = -1.75 Simplifying x = -1.75Subproblem 2
x + 1.75 = 0.0000 Simplifying x + 1.75 = 0.0000 Reorder the terms: 1.75 + x = 0.0000 Solving 1.75 + x = 0.0000 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 = 0.0000 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 0.0000 + -1.75 x = 0.0000 + -1.75 Combine like terms: 0.0000 + -1.75 = -1.75 x = -1.75 Simplifying x = -1.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.75, -1.75}
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