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Simplifying 0 = x2 + 2x + -53 Reorder the terms: 0 = -53 + 2x + x2 Solving 0 = -53 + 2x + x2 Solving for variable 'x'. Combine like terms: 0 + 53 = 53 53 + -2x + -1x2 = -53 + 2x + x2 + 53 + -2x + -1x2 Reorder the terms: 53 + -2x + -1x2 = -53 + 53 + 2x + -2x + x2 + -1x2 Combine like terms: -53 + 53 = 0 53 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 53 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 53 + -2x + -1x2 = 0 + x2 + -1x2 53 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 53 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -53 + 2x + x2 = 0 Move the constant term to the right: Add '53' to each side of the equation. -53 + 2x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 2x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 2x + x2 = 0 + 53 2x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 2x + x2 = 53 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 = 53 + 1 Reorder the terms: 1 + 2x + x2 = 53 + 1 Combine like terms: 53 + 1 = 54 1 + 2x + x2 = 54 Factor a perfect square on the left side: (x + 1)(x + 1) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + 1) equal to 7.348469228 and -7.348469228.Subproblem 1
x + 1 = 7.348469228 Simplifying x + 1 = 7.348469228 Reorder the terms: 1 + x = 7.348469228 Solving 1 + x = 7.348469228 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 = 7.348469228 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.348469228 + -1 x = 7.348469228 + -1 Combine like terms: 7.348469228 + -1 = 6.348469228 x = 6.348469228 Simplifying x = 6.348469228Subproblem 2
x + 1 = -7.348469228 Simplifying x + 1 = -7.348469228 Reorder the terms: 1 + x = -7.348469228 Solving 1 + x = -7.348469228 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 = -7.348469228 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.348469228 + -1 x = -7.348469228 + -1 Combine like terms: -7.348469228 + -1 = -8.348469228 x = -8.348469228 Simplifying x = -8.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.348469228, -8.348469228}
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