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Simplifying x2 + 6.6x + -89.11 = 0 Reorder the terms: -89.11 + 6.6x + x2 = 0 Solving -89.11 + 6.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '89.11' to each side of the equation. -89.11 + 6.6x + 89.11 + x2 = 0 + 89.11 Reorder the terms: -89.11 + 89.11 + 6.6x + x2 = 0 + 89.11 Combine like terms: -89.11 + 89.11 = 0.00 0.00 + 6.6x + x2 = 0 + 89.11 6.6x + x2 = 0 + 89.11 Combine like terms: 0 + 89.11 = 89.11 6.6x + x2 = 89.11 The x term is 6.6x. Take half its coefficient (3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. 6.6x + 10.89 + x2 = 89.11 + 10.89 Reorder the terms: 10.89 + 6.6x + x2 = 89.11 + 10.89 Combine like terms: 89.11 + 10.89 = 100 10.89 + 6.6x + x2 = 100 Factor a perfect square on the left side: (x + 3.3)(x + 3.3) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + 3.3) equal to 10 and -10.Subproblem 1
x + 3.3 = 10 Simplifying x + 3.3 = 10 Reorder the terms: 3.3 + x = 10 Solving 3.3 + x = 10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = 10 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = 10 + -3.3 x = 10 + -3.3 Combine like terms: 10 + -3.3 = 6.7 x = 6.7 Simplifying x = 6.7Subproblem 2
x + 3.3 = -10 Simplifying x + 3.3 = -10 Reorder the terms: 3.3 + x = -10 Solving 3.3 + x = -10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = -10 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = -10 + -3.3 x = -10 + -3.3 Combine like terms: -10 + -3.3 = -13.3 x = -13.3 Simplifying x = -13.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.7, -13.3}
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