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Simplifying x2 + 1.73x + -4 = 0 Reorder the terms: -4 + 1.73x + x2 = 0 Solving -4 + 1.73x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.73x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.73x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.73x + x2 = 0 + 4 1.73x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.73x + x2 = 4 The x term is 1.73x. Take half its coefficient (0.865). Square it (0.748225) and add it to both sides. Add '0.748225' to each side of the equation. 1.73x + 0.748225 + x2 = 4 + 0.748225 Reorder the terms: 0.748225 + 1.73x + x2 = 4 + 0.748225 Combine like terms: 4 + 0.748225 = 4.748225 0.748225 + 1.73x + x2 = 4.748225 Factor a perfect square on the left side: (x + 0.865)(x + 0.865) = 4.748225 Calculate the square root of the right side: 2.179042221 Break this problem into two subproblems by setting (x + 0.865) equal to 2.179042221 and -2.179042221.Subproblem 1
x + 0.865 = 2.179042221 Simplifying x + 0.865 = 2.179042221 Reorder the terms: 0.865 + x = 2.179042221 Solving 0.865 + x = 2.179042221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.865' to each side of the equation. 0.865 + -0.865 + x = 2.179042221 + -0.865 Combine like terms: 0.865 + -0.865 = 0.000 0.000 + x = 2.179042221 + -0.865 x = 2.179042221 + -0.865 Combine like terms: 2.179042221 + -0.865 = 1.314042221 x = 1.314042221 Simplifying x = 1.314042221Subproblem 2
x + 0.865 = -2.179042221 Simplifying x + 0.865 = -2.179042221 Reorder the terms: 0.865 + x = -2.179042221 Solving 0.865 + x = -2.179042221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.865' to each side of the equation. 0.865 + -0.865 + x = -2.179042221 + -0.865 Combine like terms: 0.865 + -0.865 = 0.000 0.000 + x = -2.179042221 + -0.865 x = -2.179042221 + -0.865 Combine like terms: -2.179042221 + -0.865 = -3.044042221 x = -3.044042221 Simplifying x = -3.044042221Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.314042221, -3.044042221}
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