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Simplifying x2 + 0.86x + -0.9 = 0 Reorder the terms: -0.9 + 0.86x + x2 = 0 Solving -0.9 + 0.86x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.86x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.86x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.86x + x2 = 0 + 0.9 0.86x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 0.86x + x2 = 0.9 The x term is 0.86x. Take half its coefficient (0.43). Square it (0.1849) and add it to both sides. Add '0.1849' to each side of the equation. 0.86x + 0.1849 + x2 = 0.9 + 0.1849 Reorder the terms: 0.1849 + 0.86x + x2 = 0.9 + 0.1849 Combine like terms: 0.9 + 0.1849 = 1.0849 0.1849 + 0.86x + x2 = 1.0849 Factor a perfect square on the left side: (x + 0.43)(x + 0.43) = 1.0849 Calculate the square root of the right side: 1.04158533 Break this problem into two subproblems by setting (x + 0.43) equal to 1.04158533 and -1.04158533.Subproblem 1
x + 0.43 = 1.04158533 Simplifying x + 0.43 = 1.04158533 Reorder the terms: 0.43 + x = 1.04158533 Solving 0.43 + x = 1.04158533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.43' to each side of the equation. 0.43 + -0.43 + x = 1.04158533 + -0.43 Combine like terms: 0.43 + -0.43 = 0.00 0.00 + x = 1.04158533 + -0.43 x = 1.04158533 + -0.43 Combine like terms: 1.04158533 + -0.43 = 0.61158533 x = 0.61158533 Simplifying x = 0.61158533Subproblem 2
x + 0.43 = -1.04158533 Simplifying x + 0.43 = -1.04158533 Reorder the terms: 0.43 + x = -1.04158533 Solving 0.43 + x = -1.04158533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.43' to each side of the equation. 0.43 + -0.43 + x = -1.04158533 + -0.43 Combine like terms: 0.43 + -0.43 = 0.00 0.00 + x = -1.04158533 + -0.43 x = -1.04158533 + -0.43 Combine like terms: -1.04158533 + -0.43 = -1.47158533 x = -1.47158533 Simplifying x = -1.47158533Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.61158533, -1.47158533}
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