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Simplifying x2 + -1.1x + -2.76 = 0 Reorder the terms: -2.76 + -1.1x + x2 = 0 Solving -2.76 + -1.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.76' to each side of the equation. -2.76 + -1.1x + 2.76 + x2 = 0 + 2.76 Reorder the terms: -2.76 + 2.76 + -1.1x + x2 = 0 + 2.76 Combine like terms: -2.76 + 2.76 = 0.00 0.00 + -1.1x + x2 = 0 + 2.76 -1.1x + x2 = 0 + 2.76 Combine like terms: 0 + 2.76 = 2.76 -1.1x + x2 = 2.76 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 2.76 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 2.76 + 0.3025 Combine like terms: 2.76 + 0.3025 = 3.0625 0.3025 + -1.1x + x2 = 3.0625 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 3.0625 Calculate the square root of the right side: 1.75 Break this problem into two subproblems by setting (x + -0.55) equal to 1.75 and -1.75.Subproblem 1
x + -0.55 = 1.75 Simplifying x + -0.55 = 1.75 Reorder the terms: -0.55 + x = 1.75 Solving -0.55 + x = 1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 1.75 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 1.75 + 0.55 x = 1.75 + 0.55 Combine like terms: 1.75 + 0.55 = 2.3 x = 2.3 Simplifying x = 2.3Subproblem 2
x + -0.55 = -1.75 Simplifying x + -0.55 = -1.75 Reorder the terms: -0.55 + x = -1.75 Solving -0.55 + x = -1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -1.75 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -1.75 + 0.55 x = -1.75 + 0.55 Combine like terms: -1.75 + 0.55 = -1.2 x = -1.2 Simplifying x = -1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3, -1.2}
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