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Simplifying (x * x) + 3x + -0.75 = 0 Multiply x * x (x2) + 3x + -0.75 = 0 x2 + 3x + -0.75 = 0 Reorder the terms: -0.75 + 3x + x2 = 0 Solving -0.75 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 3x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 3x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 3x + x2 = 0 + 0.75 3x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 3x + x2 = 0.75 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.75 + 2.25 Combine like terms: 0.75 + 2.25 = 3 2.25 + 3x + x2 = 3 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 1.5) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 1.5 = 1.732050808 Simplifying x + 1.5 = 1.732050808 Reorder the terms: 1.5 + x = 1.732050808 Solving 1.5 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.732050808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.732050808 + -1.5 x = 1.732050808 + -1.5 Combine like terms: 1.732050808 + -1.5 = 0.232050808 x = 0.232050808 Simplifying x = 0.232050808Subproblem 2
x + 1.5 = -1.732050808 Simplifying x + 1.5 = -1.732050808 Reorder the terms: 1.5 + x = -1.732050808 Solving 1.5 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.732050808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.732050808 + -1.5 x = -1.732050808 + -1.5 Combine like terms: -1.732050808 + -1.5 = -3.232050808 x = -3.232050808 Simplifying x = -3.232050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.232050808, -3.232050808}
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