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Simplifying 2.6x2 = 4 + -3.5x Solving 2.6x2 = 4 + -3.5x Solving for variable 'x'. Reorder the terms: -4 + 3.5x + 2.6x2 = 4 + -3.5x + -4 + 3.5x Reorder the terms: -4 + 3.5x + 2.6x2 = 4 + -4 + -3.5x + 3.5x Combine like terms: 4 + -4 = 0 -4 + 3.5x + 2.6x2 = 0 + -3.5x + 3.5x -4 + 3.5x + 2.6x2 = -3.5x + 3.5x Combine like terms: -3.5x + 3.5x = 0.0 -4 + 3.5x + 2.6x2 = 0.0 Begin completing the square. Divide all terms by 2.6 the coefficient of the squared term: Divide each side by '2.6'. -1.538461538 + 1.346153846x + x2 = 0 Move the constant term to the right: Add '1.538461538' to each side of the equation. -1.538461538 + 1.346153846x + 1.538461538 + x2 = 0 + 1.538461538 Reorder the terms: -1.538461538 + 1.538461538 + 1.346153846x + x2 = 0 + 1.538461538 Combine like terms: -1.538461538 + 1.538461538 = 0.000000000 0.000000000 + 1.346153846x + x2 = 0 + 1.538461538 1.346153846x + x2 = 0 + 1.538461538 Combine like terms: 0 + 1.538461538 = 1.538461538 1.346153846x + x2 = 1.538461538 The x term is 1.346153846x. Take half its coefficient (0.673076923). Square it (0.4530325443) and add it to both sides. Add '0.4530325443' to each side of the equation. 1.346153846x + 0.4530325443 + x2 = 1.538461538 + 0.4530325443 Reorder the terms: 0.4530325443 + 1.346153846x + x2 = 1.538461538 + 0.4530325443 Combine like terms: 1.538461538 + 0.4530325443 = 1.9914940823 0.4530325443 + 1.346153846x + x2 = 1.9914940823 Factor a perfect square on the left side: (x + 0.673076923)(x + 0.673076923) = 1.9914940823 Calculate the square root of the right side: 1.411203062 Break this problem into two subproblems by setting (x + 0.673076923) equal to 1.411203062 and -1.411203062.Subproblem 1
x + 0.673076923 = 1.411203062 Simplifying x + 0.673076923 = 1.411203062 Reorder the terms: 0.673076923 + x = 1.411203062 Solving 0.673076923 + x = 1.411203062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.673076923' to each side of the equation. 0.673076923 + -0.673076923 + x = 1.411203062 + -0.673076923 Combine like terms: 0.673076923 + -0.673076923 = 0.000000000 0.000000000 + x = 1.411203062 + -0.673076923 x = 1.411203062 + -0.673076923 Combine like terms: 1.411203062 + -0.673076923 = 0.738126139 x = 0.738126139 Simplifying x = 0.738126139Subproblem 2
x + 0.673076923 = -1.411203062 Simplifying x + 0.673076923 = -1.411203062 Reorder the terms: 0.673076923 + x = -1.411203062 Solving 0.673076923 + x = -1.411203062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.673076923' to each side of the equation. 0.673076923 + -0.673076923 + x = -1.411203062 + -0.673076923 Combine like terms: 0.673076923 + -0.673076923 = 0.000000000 0.000000000 + x = -1.411203062 + -0.673076923 x = -1.411203062 + -0.673076923 Combine like terms: -1.411203062 + -0.673076923 = -2.084279985 x = -2.084279985 Simplifying x = -2.084279985Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.738126139, -2.084279985}
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