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Simplifying 2x2 + x = 106 Reorder the terms: x + 2x2 = 106 Solving x + 2x2 = 106 Solving for variable 'x'. Reorder the terms: -106 + x + 2x2 = 106 + -106 Combine like terms: 106 + -106 = 0 -106 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -53 + 0.5x + x2 = 0 Move the constant term to the right: Add '53' to each side of the equation. -53 + 0.5x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 0.5x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 0.5x + x2 = 0 + 53 0.5x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 0.5x + x2 = 53 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 53 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 53 + 0.25 Combine like terms: 53 + 0.25 = 53.25 0.25 + 0.5x + x2 = 53.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (x + 0.5) equal to 7.29725976 and -7.29725976.Subproblem 1
x + 0.5 = 7.29725976 Simplifying x + 0.5 = 7.29725976 Reorder the terms: 0.5 + x = 7.29725976 Solving 0.5 + x = 7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.29725976 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.29725976 + -0.5 x = 7.29725976 + -0.5 Combine like terms: 7.29725976 + -0.5 = 6.79725976 x = 6.79725976 Simplifying x = 6.79725976Subproblem 2
x + 0.5 = -7.29725976 Simplifying x + 0.5 = -7.29725976 Reorder the terms: 0.5 + x = -7.29725976 Solving 0.5 + x = -7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.29725976 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.29725976 + -0.5 x = -7.29725976 + -0.5 Combine like terms: -7.29725976 + -0.5 = -7.79725976 x = -7.79725976 Simplifying x = -7.79725976Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.79725976, -7.79725976}
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