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Simplifying x2 + -1.8x + 0.155 = 0 Reorder the terms: 0.155 + -1.8x + x2 = 0 Solving 0.155 + -1.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.155' to each side of the equation. 0.155 + -1.8x + -0.155 + x2 = 0 + -0.155 Reorder the terms: 0.155 + -0.155 + -1.8x + x2 = 0 + -0.155 Combine like terms: 0.155 + -0.155 = 0.000 0.000 + -1.8x + x2 = 0 + -0.155 -1.8x + x2 = 0 + -0.155 Combine like terms: 0 + -0.155 = -0.155 -1.8x + x2 = -0.155 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = -0.155 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = -0.155 + 0.81 Combine like terms: -0.155 + 0.81 = 0.655 0.81 + -1.8x + x2 = 0.655 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 0.655 Calculate the square root of the right side: 0.809320703 Break this problem into two subproblems by setting (x + -0.9) equal to 0.809320703 and -0.809320703.Subproblem 1
x + -0.9 = 0.809320703 Simplifying x + -0.9 = 0.809320703 Reorder the terms: -0.9 + x = 0.809320703 Solving -0.9 + x = 0.809320703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.809320703 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.809320703 + 0.9 x = 0.809320703 + 0.9 Combine like terms: 0.809320703 + 0.9 = 1.709320703 x = 1.709320703 Simplifying x = 1.709320703Subproblem 2
x + -0.9 = -0.809320703 Simplifying x + -0.9 = -0.809320703 Reorder the terms: -0.9 + x = -0.809320703 Solving -0.9 + x = -0.809320703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -0.809320703 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -0.809320703 + 0.9 x = -0.809320703 + 0.9 Combine like terms: -0.809320703 + 0.9 = 0.090679297 x = 0.090679297 Simplifying x = 0.090679297Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.709320703, 0.090679297}
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