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Simplifying 5x2 = 22x + -3 Reorder the terms: 5x2 = -3 + 22x Solving 5x2 = -3 + 22x Solving for variable 'x'. Reorder the terms: 3 + -22x + 5x2 = -3 + 22x + 3 + -22x Reorder the terms: 3 + -22x + 5x2 = -3 + 3 + 22x + -22x Combine like terms: -3 + 3 = 0 3 + -22x + 5x2 = 0 + 22x + -22x 3 + -22x + 5x2 = 22x + -22x Combine like terms: 22x + -22x = 0 3 + -22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -4.4x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -4.4x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -4.4x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -4.4x + x2 = 0 + -0.6 -4.4x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -4.4x + x2 = -0.6 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 = -0.6 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = -0.6 + 4.84 Combine like terms: -0.6 + 4.84 = 4.24 4.84 + -4.4x + x2 = 4.24 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (x + -2.2) equal to 2.059126028 and -2.059126028.Subproblem 1
x + -2.2 = 2.059126028 Simplifying x + -2.2 = 2.059126028 Reorder the terms: -2.2 + x = 2.059126028 Solving -2.2 + x = 2.059126028 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 = 2.059126028 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 2.059126028 + 2.2 x = 2.059126028 + 2.2 Combine like terms: 2.059126028 + 2.2 = 4.259126028 x = 4.259126028 Simplifying x = 4.259126028Subproblem 2
x + -2.2 = -2.059126028 Simplifying x + -2.2 = -2.059126028 Reorder the terms: -2.2 + x = -2.059126028 Solving -2.2 + x = -2.059126028 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 = -2.059126028 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -2.059126028 + 2.2 x = -2.059126028 + 2.2 Combine like terms: -2.059126028 + 2.2 = 0.140873972 x = 0.140873972 Simplifying x = 0.140873972Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.259126028, 0.140873972}
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