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Simplifying x2 + 2.7x + -1.9 = 0 Reorder the terms: -1.9 + 2.7x + x2 = 0 Solving -1.9 + 2.7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + 2.7x + 1.9 + x2 = 0 + 1.9 Reorder the terms: -1.9 + 1.9 + 2.7x + x2 = 0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + 2.7x + x2 = 0 + 1.9 2.7x + x2 = 0 + 1.9 Combine like terms: 0 + 1.9 = 1.9 2.7x + x2 = 1.9 The x term is 2.7x. Take half its coefficient (1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. 2.7x + 1.8225 + x2 = 1.9 + 1.8225 Reorder the terms: 1.8225 + 2.7x + x2 = 1.9 + 1.8225 Combine like terms: 1.9 + 1.8225 = 3.7225 1.8225 + 2.7x + x2 = 3.7225 Factor a perfect square on the left side: (x + 1.35)(x + 1.35) = 3.7225 Calculate the square root of the right side: 1.929378138 Break this problem into two subproblems by setting (x + 1.35) equal to 1.929378138 and -1.929378138.Subproblem 1
x + 1.35 = 1.929378138 Simplifying x + 1.35 = 1.929378138 Reorder the terms: 1.35 + x = 1.929378138 Solving 1.35 + x = 1.929378138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + x = 1.929378138 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = 1.929378138 + -1.35 x = 1.929378138 + -1.35 Combine like terms: 1.929378138 + -1.35 = 0.579378138 x = 0.579378138 Simplifying x = 0.579378138Subproblem 2
x + 1.35 = -1.929378138 Simplifying x + 1.35 = -1.929378138 Reorder the terms: 1.35 + x = -1.929378138 Solving 1.35 + x = -1.929378138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + x = -1.929378138 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = -1.929378138 + -1.35 x = -1.929378138 + -1.35 Combine like terms: -1.929378138 + -1.35 = -3.279378138 x = -3.279378138 Simplifying x = -3.279378138Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.579378138, -3.279378138}
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