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Simplifying 10x2 + -2x + 5x + -1 + -14x = 0 Reorder the terms: -1 + -2x + 5x + -14x + 10x2 = 0 Combine like terms: -2x + 5x = 3x -1 + 3x + -14x + 10x2 = 0 Combine like terms: 3x + -14x = -11x -1 + -11x + 10x2 = 0 Solving -1 + -11x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.1 + -1.1x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -1.1x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -1.1x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -1.1x + x2 = 0 + 0.1 -1.1x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -1.1x + x2 = 0.1 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 0.1 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 0.1 + 0.3025 Combine like terms: 0.1 + 0.3025 = 0.4025 0.3025 + -1.1x + x2 = 0.4025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 0.4025 Calculate the square root of the right side: 0.634428877 Break this problem into two subproblems by setting (x + -0.55) equal to 0.634428877 and -0.634428877.Subproblem 1
x + -0.55 = 0.634428877 Simplifying x + -0.55 = 0.634428877 Reorder the terms: -0.55 + x = 0.634428877 Solving -0.55 + x = 0.634428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 0.634428877 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 0.634428877 + 0.55 x = 0.634428877 + 0.55 Combine like terms: 0.634428877 + 0.55 = 1.184428877 x = 1.184428877 Simplifying x = 1.184428877Subproblem 2
x + -0.55 = -0.634428877 Simplifying x + -0.55 = -0.634428877 Reorder the terms: -0.55 + x = -0.634428877 Solving -0.55 + x = -0.634428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -0.634428877 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -0.634428877 + 0.55 x = -0.634428877 + 0.55 Combine like terms: -0.634428877 + 0.55 = -0.084428877 x = -0.084428877 Simplifying x = -0.084428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.184428877, -0.084428877}
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