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Simplifying x2 + -1.62x + -1 = 0 Reorder the terms: -1 + -1.62x + x2 = 0 Solving -1 + -1.62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.62x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.62x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.62x + x2 = 0 + 1 -1.62x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.62x + x2 = 1 The x term is -1.62x. Take half its coefficient (-0.81). Square it (0.6561) and add it to both sides. Add '0.6561' to each side of the equation. -1.62x + 0.6561 + x2 = 1 + 0.6561 Reorder the terms: 0.6561 + -1.62x + x2 = 1 + 0.6561 Combine like terms: 1 + 0.6561 = 1.6561 0.6561 + -1.62x + x2 = 1.6561 Factor a perfect square on the left side: (x + -0.81)(x + -0.81) = 1.6561 Calculate the square root of the right side: 1.286895489 Break this problem into two subproblems by setting (x + -0.81) equal to 1.286895489 and -1.286895489.Subproblem 1
x + -0.81 = 1.286895489 Simplifying x + -0.81 = 1.286895489 Reorder the terms: -0.81 + x = 1.286895489 Solving -0.81 + x = 1.286895489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.81' to each side of the equation. -0.81 + 0.81 + x = 1.286895489 + 0.81 Combine like terms: -0.81 + 0.81 = 0.00 0.00 + x = 1.286895489 + 0.81 x = 1.286895489 + 0.81 Combine like terms: 1.286895489 + 0.81 = 2.096895489 x = 2.096895489 Simplifying x = 2.096895489Subproblem 2
x + -0.81 = -1.286895489 Simplifying x + -0.81 = -1.286895489 Reorder the terms: -0.81 + x = -1.286895489 Solving -0.81 + x = -1.286895489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.81' to each side of the equation. -0.81 + 0.81 + x = -1.286895489 + 0.81 Combine like terms: -0.81 + 0.81 = 0.00 0.00 + x = -1.286895489 + 0.81 x = -1.286895489 + 0.81 Combine like terms: -1.286895489 + 0.81 = -0.476895489 x = -0.476895489 Simplifying x = -0.476895489Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.096895489, -0.476895489}
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