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Simplifying 5x2 + -2x + -166 = 0 Reorder the terms: -166 + -2x + 5x2 = 0 Solving -166 + -2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -33.2 + -0.4x + x2 = 0 Move the constant term to the right: Add '33.2' to each side of the equation. -33.2 + -0.4x + 33.2 + x2 = 0 + 33.2 Reorder the terms: -33.2 + 33.2 + -0.4x + x2 = 0 + 33.2 Combine like terms: -33.2 + 33.2 = 0.0 0.0 + -0.4x + x2 = 0 + 33.2 -0.4x + x2 = 0 + 33.2 Combine like terms: 0 + 33.2 = 33.2 -0.4x + x2 = 33.2 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 33.2 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 33.2 + 0.04 Combine like terms: 33.2 + 0.04 = 33.24 0.04 + -0.4x + x2 = 33.24 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 33.24 Calculate the square root of the right side: 5.765414122 Break this problem into two subproblems by setting (x + -0.2) equal to 5.765414122 and -5.765414122.Subproblem 1
x + -0.2 = 5.765414122 Simplifying x + -0.2 = 5.765414122 Reorder the terms: -0.2 + x = 5.765414122 Solving -0.2 + x = 5.765414122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 5.765414122 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 5.765414122 + 0.2 x = 5.765414122 + 0.2 Combine like terms: 5.765414122 + 0.2 = 5.965414122 x = 5.965414122 Simplifying x = 5.965414122Subproblem 2
x + -0.2 = -5.765414122 Simplifying x + -0.2 = -5.765414122 Reorder the terms: -0.2 + x = -5.765414122 Solving -0.2 + x = -5.765414122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -5.765414122 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -5.765414122 + 0.2 x = -5.765414122 + 0.2 Combine like terms: -5.765414122 + 0.2 = -5.565414122 x = -5.565414122 Simplifying x = -5.565414122Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.965414122, -5.565414122}
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