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Simplifying 0.81x2 + -1.4x + -1 = 0 Reorder the terms: -1 + -1.4x + 0.81x2 = 0 Solving -1 + -1.4x + 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 + -1.728395062x + x2 = 0 Move the constant term to the right: Add '1.234567901' to each side of the equation. -1.234567901 + -1.728395062x + 1.234567901 + x2 = 0 + 1.234567901 Reorder the terms: -1.234567901 + 1.234567901 + -1.728395062x + x2 = 0 + 1.234567901 Combine like terms: -1.234567901 + 1.234567901 = 0.000000000 0.000000000 + -1.728395062x + x2 = 0 + 1.234567901 -1.728395062x + x2 = 0 + 1.234567901 Combine like terms: 0 + 1.234567901 = 1.234567901 -1.728395062x + x2 = 1.234567901 The x term is -1.728395062x. Take half its coefficient (-0.864197531). Square it (0.7468373726) and add it to both sides. Add '0.7468373726' to each side of the equation. -1.728395062x + 0.7468373726 + x2 = 1.234567901 + 0.7468373726 Reorder the terms: 0.7468373726 + -1.728395062x + x2 = 1.234567901 + 0.7468373726 Combine like terms: 1.234567901 + 0.7468373726 = 1.9814052736 0.7468373726 + -1.728395062x + x2 = 1.9814052736 Factor a perfect square on the left side: (x + -0.864197531)(x + -0.864197531) = 1.9814052736 Calculate the square root of the right side: 1.407623982 Break this problem into two subproblems by setting (x + -0.864197531) equal to 1.407623982 and -1.407623982.Subproblem 1
x + -0.864197531 = 1.407623982 Simplifying x + -0.864197531 = 1.407623982 Reorder the terms: -0.864197531 + x = 1.407623982 Solving -0.864197531 + x = 1.407623982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.864197531' to each side of the equation. -0.864197531 + 0.864197531 + x = 1.407623982 + 0.864197531 Combine like terms: -0.864197531 + 0.864197531 = 0.000000000 0.000000000 + x = 1.407623982 + 0.864197531 x = 1.407623982 + 0.864197531 Combine like terms: 1.407623982 + 0.864197531 = 2.271821513 x = 2.271821513 Simplifying x = 2.271821513Subproblem 2
x + -0.864197531 = -1.407623982 Simplifying x + -0.864197531 = -1.407623982 Reorder the terms: -0.864197531 + x = -1.407623982 Solving -0.864197531 + x = -1.407623982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.864197531' to each side of the equation. -0.864197531 + 0.864197531 + x = -1.407623982 + 0.864197531 Combine like terms: -0.864197531 + 0.864197531 = 0.000000000 0.000000000 + x = -1.407623982 + 0.864197531 x = -1.407623982 + 0.864197531 Combine like terms: -1.407623982 + 0.864197531 = -0.543426451 x = -0.543426451 Simplifying x = -0.543426451Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.271821513, -0.543426451}
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