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Simplifying x2 + 6x + -142 = 0 Reorder the terms: -142 + 6x + x2 = 0 Solving -142 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + 6x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + 6x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + 6x + x2 = 0 + 142 6x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 6x + x2 = 142 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 142 + 9 Reorder the terms: 9 + 6x + x2 = 142 + 9 Combine like terms: 142 + 9 = 151 9 + 6x + x2 = 151 Factor a perfect square on the left side: (x + 3)(x + 3) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + 3) equal to 12.288205727 and -12.288205727.Subproblem 1
x + 3 = 12.288205727 Simplifying x + 3 = 12.288205727 Reorder the terms: 3 + x = 12.288205727 Solving 3 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 12.288205727 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.288205727 + -3 x = 12.288205727 + -3 Combine like terms: 12.288205727 + -3 = 9.288205727 x = 9.288205727 Simplifying x = 9.288205727Subproblem 2
x + 3 = -12.288205727 Simplifying x + 3 = -12.288205727 Reorder the terms: 3 + x = -12.288205727 Solving 3 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -12.288205727 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.288205727 + -3 x = -12.288205727 + -3 Combine like terms: -12.288205727 + -3 = -15.288205727 x = -15.288205727 Simplifying x = -15.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.288205727, -15.288205727}
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