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Simplifying x2 + 0.75x + -16 = 0 Reorder the terms: -16 + 0.75x + x2 = 0 Solving -16 + 0.75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 0.75x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 0.75x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 0.75x + x2 = 0 + 16 0.75x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 0.75x + x2 = 16 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 16 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 16 + 0.140625 Combine like terms: 16 + 0.140625 = 16.140625 0.140625 + 0.75x + x2 = 16.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 16.140625 Calculate the square root of the right side: 4.01753967 Break this problem into two subproblems by setting (x + 0.375) equal to 4.01753967 and -4.01753967.Subproblem 1
x + 0.375 = 4.01753967 Simplifying x + 0.375 = 4.01753967 Reorder the terms: 0.375 + x = 4.01753967 Solving 0.375 + x = 4.01753967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 4.01753967 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 4.01753967 + -0.375 x = 4.01753967 + -0.375 Combine like terms: 4.01753967 + -0.375 = 3.64253967 x = 3.64253967 Simplifying x = 3.64253967Subproblem 2
x + 0.375 = -4.01753967 Simplifying x + 0.375 = -4.01753967 Reorder the terms: 0.375 + x = -4.01753967 Solving 0.375 + x = -4.01753967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -4.01753967 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -4.01753967 + -0.375 x = -4.01753967 + -0.375 Combine like terms: -4.01753967 + -0.375 = -4.39253967 x = -4.39253967 Simplifying x = -4.39253967Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.64253967, -4.39253967}
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