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Simplifying 1.56x2 + -4.38x + -0.94 = 0 Reorder the terms: -0.94 + -4.38x + 1.56x2 = 0 Solving -0.94 + -4.38x + 1.56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.56 the coefficient of the squared term: Divide each side by '1.56'. -0.6025641026 + -2.807692308x + x2 = 0 Move the constant term to the right: Add '0.6025641026' to each side of the equation. -0.6025641026 + -2.807692308x + 0.6025641026 + x2 = 0 + 0.6025641026 Reorder the terms: -0.6025641026 + 0.6025641026 + -2.807692308x + x2 = 0 + 0.6025641026 Combine like terms: -0.6025641026 + 0.6025641026 = 0.0000000000 0.0000000000 + -2.807692308x + x2 = 0 + 0.6025641026 -2.807692308x + x2 = 0 + 0.6025641026 Combine like terms: 0 + 0.6025641026 = 0.6025641026 -2.807692308x + x2 = 0.6025641026 The x term is -2.807692308x. Take half its coefficient (-1.403846154). Square it (1.970784024) and add it to both sides. Add '1.970784024' to each side of the equation. -2.807692308x + 1.970784024 + x2 = 0.6025641026 + 1.970784024 Reorder the terms: 1.970784024 + -2.807692308x + x2 = 0.6025641026 + 1.970784024 Combine like terms: 0.6025641026 + 1.970784024 = 2.5733481266 1.970784024 + -2.807692308x + x2 = 2.5733481266 Factor a perfect square on the left side: (x + -1.403846154)(x + -1.403846154) = 2.5733481266 Calculate the square root of the right side: 1.604165866 Break this problem into two subproblems by setting (x + -1.403846154) equal to 1.604165866 and -1.604165866.Subproblem 1
x + -1.403846154 = 1.604165866 Simplifying x + -1.403846154 = 1.604165866 Reorder the terms: -1.403846154 + x = 1.604165866 Solving -1.403846154 + x = 1.604165866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.403846154' to each side of the equation. -1.403846154 + 1.403846154 + x = 1.604165866 + 1.403846154 Combine like terms: -1.403846154 + 1.403846154 = 0.000000000 0.000000000 + x = 1.604165866 + 1.403846154 x = 1.604165866 + 1.403846154 Combine like terms: 1.604165866 + 1.403846154 = 3.00801202 x = 3.00801202 Simplifying x = 3.00801202Subproblem 2
x + -1.403846154 = -1.604165866 Simplifying x + -1.403846154 = -1.604165866 Reorder the terms: -1.403846154 + x = -1.604165866 Solving -1.403846154 + x = -1.604165866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.403846154' to each side of the equation. -1.403846154 + 1.403846154 + x = -1.604165866 + 1.403846154 Combine like terms: -1.403846154 + 1.403846154 = 0.000000000 0.000000000 + x = -1.604165866 + 1.403846154 x = -1.604165866 + 1.403846154 Combine like terms: -1.604165866 + 1.403846154 = -0.200319712 x = -0.200319712 Simplifying x = -0.200319712Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.00801202, -0.200319712}
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