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Simplifying 1 + 1.8x + -0.81x2 = 0 Solving 1 + 1.8x + -0.81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.81 the coefficient of the squared term: Divide each side by '-0.81'. -1.234567901 + -2.222222222x + x2 = 0 Move the constant term to the right: Add '1.234567901' to each side of the equation. -1.234567901 + -2.222222222x + 1.234567901 + x2 = 0 + 1.234567901 Reorder the terms: -1.234567901 + 1.234567901 + -2.222222222x + x2 = 0 + 1.234567901 Combine like terms: -1.234567901 + 1.234567901 = 0.000000000 0.000000000 + -2.222222222x + x2 = 0 + 1.234567901 -2.222222222x + x2 = 0 + 1.234567901 Combine like terms: 0 + 1.234567901 = 1.234567901 -2.222222222x + x2 = 1.234567901 The x term is -2.222222222x. Take half its coefficient (-1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. -2.222222222x + 1.234567901 + x2 = 1.234567901 + 1.234567901 Reorder the terms: 1.234567901 + -2.222222222x + x2 = 1.234567901 + 1.234567901 Combine like terms: 1.234567901 + 1.234567901 = 2.469135802 1.234567901 + -2.222222222x + x2 = 2.469135802 Factor a perfect square on the left side: (x + -1.111111111)(x + -1.111111111) = 2.469135802 Calculate the square root of the right side: 1.571348402 Break this problem into two subproblems by setting (x + -1.111111111) equal to 1.571348402 and -1.571348402.Subproblem 1
x + -1.111111111 = 1.571348402 Simplifying x + -1.111111111 = 1.571348402 Reorder the terms: -1.111111111 + x = 1.571348402 Solving -1.111111111 + x = 1.571348402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = 1.571348402 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = 1.571348402 + 1.111111111 x = 1.571348402 + 1.111111111 Combine like terms: 1.571348402 + 1.111111111 = 2.682459513 x = 2.682459513 Simplifying x = 2.682459513Subproblem 2
x + -1.111111111 = -1.571348402 Simplifying x + -1.111111111 = -1.571348402 Reorder the terms: -1.111111111 + x = -1.571348402 Solving -1.111111111 + x = -1.571348402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = -1.571348402 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = -1.571348402 + 1.111111111 x = -1.571348402 + 1.111111111 Combine like terms: -1.571348402 + 1.111111111 = -0.460237291 x = -0.460237291 Simplifying x = -0.460237291Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.682459513, -0.460237291}
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