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Simplifying 0.2466 + -1.8x = x2 Solving 0.2466 + -1.8x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.2466 + -1.8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.2466 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.2466' to each side of the equation. -0.2466 + 1.8x + 0.2466 + x2 = 0 + 0.2466 Reorder the terms: -0.2466 + 0.2466 + 1.8x + x2 = 0 + 0.2466 Combine like terms: -0.2466 + 0.2466 = 0.0000 0.0000 + 1.8x + x2 = 0 + 0.2466 1.8x + x2 = 0 + 0.2466 Combine like terms: 0 + 0.2466 = 0.2466 1.8x + x2 = 0.2466 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.2466 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.2466 + 0.81 Combine like terms: 0.2466 + 0.81 = 1.0566 0.81 + 1.8x + x2 = 1.0566 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.0566 Calculate the square root of the right side: 1.027910502 Break this problem into two subproblems by setting (x + 0.9) equal to 1.027910502 and -1.027910502.Subproblem 1
x + 0.9 = 1.027910502 Simplifying x + 0.9 = 1.027910502 Reorder the terms: 0.9 + x = 1.027910502 Solving 0.9 + x = 1.027910502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.027910502 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.027910502 + -0.9 x = 1.027910502 + -0.9 Combine like terms: 1.027910502 + -0.9 = 0.127910502 x = 0.127910502 Simplifying x = 0.127910502Subproblem 2
x + 0.9 = -1.027910502 Simplifying x + 0.9 = -1.027910502 Reorder the terms: 0.9 + x = -1.027910502 Solving 0.9 + x = -1.027910502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.027910502 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.027910502 + -0.9 x = -1.027910502 + -0.9 Combine like terms: -1.027910502 + -0.9 = -1.927910502 x = -1.927910502 Simplifying x = -1.927910502Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.127910502, -1.927910502}
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