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Simplifying x2 + -3x + 1.05 = 0 Reorder the terms: 1.05 + -3x + x2 = 0 Solving 1.05 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.05' to each side of the equation. 1.05 + -3x + -1.05 + x2 = 0 + -1.05 Reorder the terms: 1.05 + -1.05 + -3x + x2 = 0 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + -3x + x2 = 0 + -1.05 -3x + x2 = 0 + -1.05 Combine like terms: 0 + -1.05 = -1.05 -3x + x2 = -1.05 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 = -1.05 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.05 + 2.25 Combine like terms: -1.05 + 2.25 = 1.2 2.25 + -3x + x2 = 1.2 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (x + -1.5) equal to 1.095445115 and -1.095445115.Subproblem 1
x + -1.5 = 1.095445115 Simplifying x + -1.5 = 1.095445115 Reorder the terms: -1.5 + x = 1.095445115 Solving -1.5 + x = 1.095445115 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 = 1.095445115 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.095445115 + 1.5 x = 1.095445115 + 1.5 Combine like terms: 1.095445115 + 1.5 = 2.595445115 x = 2.595445115 Simplifying x = 2.595445115Subproblem 2
x + -1.5 = -1.095445115 Simplifying x + -1.5 = -1.095445115 Reorder the terms: -1.5 + x = -1.095445115 Solving -1.5 + x = -1.095445115 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 = -1.095445115 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.095445115 + 1.5 x = -1.095445115 + 1.5 Combine like terms: -1.095445115 + 1.5 = 0.404554885 x = 0.404554885 Simplifying x = 0.404554885Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.595445115, 0.404554885}
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