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Simplifying 5x2 + -22 = -10x Reorder the terms: -22 + 5x2 = -10x Solving -22 + 5x2 = -10x Solving for variable 'x'. Reorder the terms: -22 + 10x + 5x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -22 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.4 + 2x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + 2x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + 2x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + 2x + x2 = 0 + 4.4 2x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 2x + x2 = 4.4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 4.4 + 1 Reorder the terms: 1 + 2x + x2 = 4.4 + 1 Combine like terms: 4.4 + 1 = 5.4 1 + 2x + x2 = 5.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 5.4 Calculate the square root of the right side: 2.323790008 Break this problem into two subproblems by setting (x + 1) equal to 2.323790008 and -2.323790008.Subproblem 1
x + 1 = 2.323790008 Simplifying x + 1 = 2.323790008 Reorder the terms: 1 + x = 2.323790008 Solving 1 + x = 2.323790008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.323790008 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.323790008 + -1 x = 2.323790008 + -1 Combine like terms: 2.323790008 + -1 = 1.323790008 x = 1.323790008 Simplifying x = 1.323790008Subproblem 2
x + 1 = -2.323790008 Simplifying x + 1 = -2.323790008 Reorder the terms: 1 + x = -2.323790008 Solving 1 + x = -2.323790008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.323790008 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.323790008 + -1 x = -2.323790008 + -1 Combine like terms: -2.323790008 + -1 = -3.323790008 x = -3.323790008 Simplifying x = -3.323790008Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.323790008, -3.323790008}
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