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Simplifying 0.120582 + -1.80x + -1x2 = 0 Solving 0.120582 + -1.80x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.120582 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.120582' to each side of the equation. -0.120582 + 1.8x + 0.120582 + x2 = 0 + 0.120582 Reorder the terms: -0.120582 + 0.120582 + 1.8x + x2 = 0 + 0.120582 Combine like terms: -0.120582 + 0.120582 = 0.000000 0.000000 + 1.8x + x2 = 0 + 0.120582 1.8x + x2 = 0 + 0.120582 Combine like terms: 0 + 0.120582 = 0.120582 1.8x + x2 = 0.120582 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 = 0.120582 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.120582 + 0.81 Combine like terms: 0.120582 + 0.81 = 0.930582 0.81 + 1.8x + x2 = 0.930582 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.930582 Calculate the square root of the right side: 0.964666782 Break this problem into two subproblems by setting (x + 0.9) equal to 0.964666782 and -0.964666782.Subproblem 1
x + 0.9 = 0.964666782 Simplifying x + 0.9 = 0.964666782 Reorder the terms: 0.9 + x = 0.964666782 Solving 0.9 + x = 0.964666782 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 = 0.964666782 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.964666782 + -0.9 x = 0.964666782 + -0.9 Combine like terms: 0.964666782 + -0.9 = 0.064666782 x = 0.064666782 Simplifying x = 0.064666782Subproblem 2
x + 0.9 = -0.964666782 Simplifying x + 0.9 = -0.964666782 Reorder the terms: 0.9 + x = -0.964666782 Solving 0.9 + x = -0.964666782 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 = -0.964666782 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.964666782 + -0.9 x = -0.964666782 + -0.9 Combine like terms: -0.964666782 + -0.9 = -1.864666782 x = -1.864666782 Simplifying x = -1.864666782Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.064666782, -1.864666782}
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