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Simplifying x2 + (-10.7) * x + (-95.7) = 0 x2 + -10.7x + -95.7 = 0 Reorder the terms: -95.7 + -10.7x + x2 = 0 Solving -95.7 + -10.7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '95.7' to each side of the equation. -95.7 + -10.7x + 95.7 + x2 = 0 + 95.7 Reorder the terms: -95.7 + 95.7 + -10.7x + x2 = 0 + 95.7 Combine like terms: -95.7 + 95.7 = 0.0 0.0 + -10.7x + x2 = 0 + 95.7 -10.7x + x2 = 0 + 95.7 Combine like terms: 0 + 95.7 = 95.7 -10.7x + x2 = 95.7 The x term is -10.7x. Take half its coefficient (-5.35). Square it (28.6225) and add it to both sides. Add '28.6225' to each side of the equation. -10.7x + 28.6225 + x2 = 95.7 + 28.6225 Reorder the terms: 28.6225 + -10.7x + x2 = 95.7 + 28.6225 Combine like terms: 95.7 + 28.6225 = 124.3225 28.6225 + -10.7x + x2 = 124.3225 Factor a perfect square on the left side: (x + -5.35)(x + -5.35) = 124.3225 Calculate the square root of the right side: 11.15 Break this problem into two subproblems by setting (x + -5.35) equal to 11.15 and -11.15.Subproblem 1
x + -5.35 = 11.15 Simplifying x + -5.35 = 11.15 Reorder the terms: -5.35 + x = 11.15 Solving -5.35 + x = 11.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.35' to each side of the equation. -5.35 + 5.35 + x = 11.15 + 5.35 Combine like terms: -5.35 + 5.35 = 0.00 0.00 + x = 11.15 + 5.35 x = 11.15 + 5.35 Combine like terms: 11.15 + 5.35 = 16.5 x = 16.5 Simplifying x = 16.5Subproblem 2
x + -5.35 = -11.15 Simplifying x + -5.35 = -11.15 Reorder the terms: -5.35 + x = -11.15 Solving -5.35 + x = -11.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.35' to each side of the equation. -5.35 + 5.35 + x = -11.15 + 5.35 Combine like terms: -5.35 + 5.35 = 0.00 0.00 + x = -11.15 + 5.35 x = -11.15 + 5.35 Combine like terms: -11.15 + 5.35 = -5.8 x = -5.8 Simplifying x = -5.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.5, -5.8}
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