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Simplifying x2 + 3.4x + -2.89 = 8.89 Reorder the terms: -2.89 + 3.4x + x2 = 8.89 Solving -2.89 + 3.4x + x2 = 8.89 Solving for variable 'x'. Reorder the terms: -2.89 + -8.89 + 3.4x + x2 = 8.89 + -8.89 Combine like terms: -2.89 + -8.89 = -11.78 -11.78 + 3.4x + x2 = 8.89 + -8.89 Combine like terms: 8.89 + -8.89 = 0.00 -11.78 + 3.4x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '11.78' to each side of the equation. -11.78 + 3.4x + 11.78 + x2 = 0.00 + 11.78 Reorder the terms: -11.78 + 11.78 + 3.4x + x2 = 0.00 + 11.78 Combine like terms: -11.78 + 11.78 = 0.00 0.00 + 3.4x + x2 = 0.00 + 11.78 3.4x + x2 = 0.00 + 11.78 Combine like terms: 0.00 + 11.78 = 11.78 3.4x + x2 = 11.78 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = 11.78 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = 11.78 + 2.89 Combine like terms: 11.78 + 2.89 = 14.67 2.89 + 3.4x + x2 = 14.67 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 14.67 Calculate the square root of the right side: 3.8301436 Break this problem into two subproblems by setting (x + 1.7) equal to 3.8301436 and -3.8301436.Subproblem 1
x + 1.7 = 3.8301436 Simplifying x + 1.7 = 3.8301436 Reorder the terms: 1.7 + x = 3.8301436 Solving 1.7 + x = 3.8301436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 3.8301436 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 3.8301436 + -1.7 x = 3.8301436 + -1.7 Combine like terms: 3.8301436 + -1.7 = 2.1301436 x = 2.1301436 Simplifying x = 2.1301436Subproblem 2
x + 1.7 = -3.8301436 Simplifying x + 1.7 = -3.8301436 Reorder the terms: 1.7 + x = -3.8301436 Solving 1.7 + x = -3.8301436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -3.8301436 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -3.8301436 + -1.7 x = -3.8301436 + -1.7 Combine like terms: -3.8301436 + -1.7 = -5.5301436 x = -5.5301436 Simplifying x = -5.5301436Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1301436, -5.5301436}
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