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Simplifying 5x2 + 22x + -14 = 0 Reorder the terms: -14 + 22x + 5x2 = 0 Solving -14 + 22x + 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'. -2.8 + 4.4x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 4.4x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 4.4x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 4.4x + x2 = 0 + 2.8 4.4x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 4.4x + x2 = 2.8 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = 2.8 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = 2.8 + 4.84 Combine like terms: 2.8 + 4.84 = 7.64 4.84 + 4.4x + x2 = 7.64 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 7.64 Calculate the square root of the right side: 2.764054992 Break this problem into two subproblems by setting (x + 2.2) equal to 2.764054992 and -2.764054992.Subproblem 1
x + 2.2 = 2.764054992 Simplifying x + 2.2 = 2.764054992 Reorder the terms: 2.2 + x = 2.764054992 Solving 2.2 + x = 2.764054992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 2.764054992 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 2.764054992 + -2.2 x = 2.764054992 + -2.2 Combine like terms: 2.764054992 + -2.2 = 0.564054992 x = 0.564054992 Simplifying x = 0.564054992Subproblem 2
x + 2.2 = -2.764054992 Simplifying x + 2.2 = -2.764054992 Reorder the terms: 2.2 + x = -2.764054992 Solving 2.2 + x = -2.764054992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -2.764054992 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -2.764054992 + -2.2 x = -2.764054992 + -2.2 Combine like terms: -2.764054992 + -2.2 = -4.964054992 x = -4.964054992 Simplifying x = -4.964054992Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.564054992, -4.964054992}
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