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Simplifying -5x2 + -14x + 11 = 0 Reorder the terms: 11 + -14x + -5x2 = 0 Solving 11 + -14x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.2 + 2.8x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 2.8x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 2.8x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 2.8x + x2 = 0 + 2.2 2.8x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 2.8x + x2 = 2.2 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 2.2 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 2.2 + 1.96 Combine like terms: 2.2 + 1.96 = 4.16 1.96 + 2.8x + x2 = 4.16 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 4.16 Calculate the square root of the right side: 2.039607805 Break this problem into two subproblems by setting (x + 1.4) equal to 2.039607805 and -2.039607805.Subproblem 1
x + 1.4 = 2.039607805 Simplifying x + 1.4 = 2.039607805 Reorder the terms: 1.4 + x = 2.039607805 Solving 1.4 + x = 2.039607805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 2.039607805 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 2.039607805 + -1.4 x = 2.039607805 + -1.4 Combine like terms: 2.039607805 + -1.4 = 0.639607805 x = 0.639607805 Simplifying x = 0.639607805Subproblem 2
x + 1.4 = -2.039607805 Simplifying x + 1.4 = -2.039607805 Reorder the terms: 1.4 + x = -2.039607805 Solving 1.4 + x = -2.039607805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -2.039607805 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -2.039607805 + -1.4 x = -2.039607805 + -1.4 Combine like terms: -2.039607805 + -1.4 = -3.439607805 x = -3.439607805 Simplifying x = -3.439607805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.639607805, -3.439607805}
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