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Simplifying 5x2 + -7x + 2.2 = 0 Reorder the terms: 2.2 + -7x + 5x2 = 0 Solving 2.2 + -7x + 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'. 0.44 + -1.4x + x2 = 0 Move the constant term to the right: Add '-0.44' to each side of the equation. 0.44 + -1.4x + -0.44 + x2 = 0 + -0.44 Reorder the terms: 0.44 + -0.44 + -1.4x + x2 = 0 + -0.44 Combine like terms: 0.44 + -0.44 = 0.00 0.00 + -1.4x + x2 = 0 + -0.44 -1.4x + x2 = 0 + -0.44 Combine like terms: 0 + -0.44 = -0.44 -1.4x + x2 = -0.44 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -0.44 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.44 + 0.49 Combine like terms: -0.44 + 0.49 = 0.05 0.49 + -1.4x + x2 = 0.05 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.05 Calculate the square root of the right side: 0.223606798 Break this problem into two subproblems by setting (x + -0.7) equal to 0.223606798 and -0.223606798.Subproblem 1
x + -0.7 = 0.223606798 Simplifying x + -0.7 = 0.223606798 Reorder the terms: -0.7 + x = 0.223606798 Solving -0.7 + x = 0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.223606798 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.223606798 + 0.7 x = 0.223606798 + 0.7 Combine like terms: 0.223606798 + 0.7 = 0.923606798 x = 0.923606798 Simplifying x = 0.923606798Subproblem 2
x + -0.7 = -0.223606798 Simplifying x + -0.7 = -0.223606798 Reorder the terms: -0.7 + x = -0.223606798 Solving -0.7 + x = -0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.223606798 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.223606798 + 0.7 x = -0.223606798 + 0.7 Combine like terms: -0.223606798 + 0.7 = 0.476393202 x = 0.476393202 Simplifying x = 0.476393202Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.923606798, 0.476393202}
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