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Simplifying x2 + 0.03x + -1.72 = 0 Reorder the terms: -1.72 + 0.03x + x2 = 0 Solving -1.72 + 0.03x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.72' to each side of the equation. -1.72 + 0.03x + 1.72 + x2 = 0 + 1.72 Reorder the terms: -1.72 + 1.72 + 0.03x + x2 = 0 + 1.72 Combine like terms: -1.72 + 1.72 = 0.00 0.00 + 0.03x + x2 = 0 + 1.72 0.03x + x2 = 0 + 1.72 Combine like terms: 0 + 1.72 = 1.72 0.03x + x2 = 1.72 The x term is 0.03x. Take half its coefficient (0.015). Square it (0.000225) and add it to both sides. Add '0.000225' to each side of the equation. 0.03x + 0.000225 + x2 = 1.72 + 0.000225 Reorder the terms: 0.000225 + 0.03x + x2 = 1.72 + 0.000225 Combine like terms: 1.72 + 0.000225 = 1.720225 0.000225 + 0.03x + x2 = 1.720225 Factor a perfect square on the left side: (x + 0.015)(x + 0.015) = 1.720225 Calculate the square root of the right side: 1.311573483 Break this problem into two subproblems by setting (x + 0.015) equal to 1.311573483 and -1.311573483.Subproblem 1
x + 0.015 = 1.311573483 Simplifying x + 0.015 = 1.311573483 Reorder the terms: 0.015 + x = 1.311573483 Solving 0.015 + x = 1.311573483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015' to each side of the equation. 0.015 + -0.015 + x = 1.311573483 + -0.015 Combine like terms: 0.015 + -0.015 = 0.000 0.000 + x = 1.311573483 + -0.015 x = 1.311573483 + -0.015 Combine like terms: 1.311573483 + -0.015 = 1.296573483 x = 1.296573483 Simplifying x = 1.296573483Subproblem 2
x + 0.015 = -1.311573483 Simplifying x + 0.015 = -1.311573483 Reorder the terms: 0.015 + x = -1.311573483 Solving 0.015 + x = -1.311573483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015' to each side of the equation. 0.015 + -0.015 + x = -1.311573483 + -0.015 Combine like terms: 0.015 + -0.015 = 0.000 0.000 + x = -1.311573483 + -0.015 x = -1.311573483 + -0.015 Combine like terms: -1.311573483 + -0.015 = -1.326573483 x = -1.326573483 Simplifying x = -1.326573483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.296573483, -1.326573483}
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