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Simplifying x2 + 14x + -56 = 0 Reorder the terms: -56 + 14x + x2 = 0 Solving -56 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 14x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 14x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 14x + x2 = 0 + 56 14x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 14x + x2 = 56 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 56 + 49 Reorder the terms: 49 + 14x + x2 = 56 + 49 Combine like terms: 56 + 49 = 105 49 + 14x + x2 = 105 Factor a perfect square on the left side: (x + 7)(x + 7) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 7) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 7 = 10.246950766 Simplifying x + 7 = 10.246950766 Reorder the terms: 7 + x = 10.246950766 Solving 7 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 10.246950766 + -7 Combine like terms: 7 + -7 = 0 0 + x = 10.246950766 + -7 x = 10.246950766 + -7 Combine like terms: 10.246950766 + -7 = 3.246950766 x = 3.246950766 Simplifying x = 3.246950766Subproblem 2
x + 7 = -10.246950766 Simplifying x + 7 = -10.246950766 Reorder the terms: 7 + x = -10.246950766 Solving 7 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -10.246950766 + -7 Combine like terms: 7 + -7 = 0 0 + x = -10.246950766 + -7 x = -10.246950766 + -7 Combine like terms: -10.246950766 + -7 = -17.246950766 x = -17.246950766 Simplifying x = -17.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.246950766, -17.246950766}
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