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Simplifying 10x2 + -11 + -6 = (5x + 2) Reorder the terms: -11 + -6 + 10x2 = (5x + 2) Combine like terms: -11 + -6 = -17 -17 + 10x2 = (5x + 2) Reorder the terms: -17 + 10x2 = (2 + 5x) Remove parenthesis around (2 + 5x) -17 + 10x2 = 2 + 5x Solving -17 + 10x2 = 2 + 5x Solving for variable 'x'. Reorder the terms: -17 + -2 + -5x + 10x2 = 2 + 5x + -2 + -5x Combine like terms: -17 + -2 = -19 -19 + -5x + 10x2 = 2 + 5x + -2 + -5x Reorder the terms: -19 + -5x + 10x2 = 2 + -2 + 5x + -5x Combine like terms: 2 + -2 = 0 -19 + -5x + 10x2 = 0 + 5x + -5x -19 + -5x + 10x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -19 + -5x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.9 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + -0.5x + 1.9 + x2 = 0 + 1.9 Reorder the terms: -1.9 + 1.9 + -0.5x + x2 = 0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + -0.5x + x2 = 0 + 1.9 -0.5x + x2 = 0 + 1.9 Combine like terms: 0 + 1.9 = 1.9 -0.5x + x2 = 1.9 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.9 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.9 + 0.0625 Combine like terms: 1.9 + 0.0625 = 1.9625 0.0625 + -0.5x + x2 = 1.9625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.9625 Calculate the square root of the right side: 1.400892573 Break this problem into two subproblems by setting (x + -0.25) equal to 1.400892573 and -1.400892573.Subproblem 1
x + -0.25 = 1.400892573 Simplifying x + -0.25 = 1.400892573 Reorder the terms: -0.25 + x = 1.400892573 Solving -0.25 + x = 1.400892573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.400892573 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.400892573 + 0.25 x = 1.400892573 + 0.25 Combine like terms: 1.400892573 + 0.25 = 1.650892573 x = 1.650892573 Simplifying x = 1.650892573Subproblem 2
x + -0.25 = -1.400892573 Simplifying x + -0.25 = -1.400892573 Reorder the terms: -0.25 + x = -1.400892573 Solving -0.25 + x = -1.400892573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.400892573 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.400892573 + 0.25 x = -1.400892573 + 0.25 Combine like terms: -1.400892573 + 0.25 = -1.150892573 x = -1.150892573 Simplifying x = -1.150892573Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.650892573, -1.150892573}
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