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Simplifying x2 + 4x + 3.75 = 0 Reorder the terms: 3.75 + 4x + x2 = 0 Solving 3.75 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 4x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 4x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 4x + x2 = 0 + -3.75 4x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 4x + x2 = -3.75 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.75 + 4 Reorder the terms: 4 + 4x + x2 = -3.75 + 4 Combine like terms: -3.75 + 4 = 0.25 4 + 4x + x2 = 0.25 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + 2) equal to 0.5 and -0.5.Subproblem 1
x + 2 = 0.5 Simplifying x + 2 = 0.5 Reorder the terms: 2 + x = 0.5 Solving 2 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.5 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.5 + -2 x = 0.5 + -2 Combine like terms: 0.5 + -2 = -1.5 x = -1.5 Simplifying x = -1.5Subproblem 2
x + 2 = -0.5 Simplifying x + 2 = -0.5 Reorder the terms: 2 + x = -0.5 Solving 2 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.5 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.5 + -2 x = -0.5 + -2 Combine like terms: -0.5 + -2 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.5, -2.5}
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