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Simplifying (5x + -1) + (10x2 + 7x) = 0 Reorder the terms: (-1 + 5x) + (10x2 + 7x) = 0 Remove parenthesis around (-1 + 5x) -1 + 5x + (10x2 + 7x) = 0 Reorder the terms: -1 + 5x + (7x + 10x2) = 0 Remove parenthesis around (7x + 10x2) -1 + 5x + 7x + 10x2 = 0 Combine like terms: 5x + 7x = 12x -1 + 12x + 10x2 = 0 Solving -1 + 12x + 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 + 1.2x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 1.2x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 1.2x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 1.2x + x2 = 0 + 0.1 1.2x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 1.2x + x2 = 0.1 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 0.1 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.1 + 0.36 Combine like terms: 0.1 + 0.36 = 0.46 0.36 + 1.2x + x2 = 0.46 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.46 Calculate the square root of the right side: 0.678232998 Break this problem into two subproblems by setting (x + 0.6) equal to 0.678232998 and -0.678232998.Subproblem 1
x + 0.6 = 0.678232998 Simplifying x + 0.6 = 0.678232998 Reorder the terms: 0.6 + x = 0.678232998 Solving 0.6 + x = 0.678232998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.678232998 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.678232998 + -0.6 x = 0.678232998 + -0.6 Combine like terms: 0.678232998 + -0.6 = 0.078232998 x = 0.078232998 Simplifying x = 0.078232998Subproblem 2
x + 0.6 = -0.678232998 Simplifying x + 0.6 = -0.678232998 Reorder the terms: 0.6 + x = -0.678232998 Solving 0.6 + x = -0.678232998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.678232998 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.678232998 + -0.6 x = -0.678232998 + -0.6 Combine like terms: -0.678232998 + -0.6 = -1.278232998 x = -1.278232998 Simplifying x = -1.278232998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.078232998, -1.278232998}
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