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Simplifying x2 + 14x + -75 = 0 Reorder the terms: -75 + 14x + x2 = 0 Solving -75 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 14x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 14x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 14x + x2 = 0 + 75 14x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 14x + x2 = 75 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 = 75 + 49 Reorder the terms: 49 + 14x + x2 = 75 + 49 Combine like terms: 75 + 49 = 124 49 + 14x + x2 = 124 Factor a perfect square on the left side: (x + 7)(x + 7) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + 7) equal to 11.135528726 and -11.135528726.Subproblem 1
x + 7 = 11.135528726 Simplifying x + 7 = 11.135528726 Reorder the terms: 7 + x = 11.135528726 Solving 7 + x = 11.135528726 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 = 11.135528726 + -7 Combine like terms: 7 + -7 = 0 0 + x = 11.135528726 + -7 x = 11.135528726 + -7 Combine like terms: 11.135528726 + -7 = 4.135528726 x = 4.135528726 Simplifying x = 4.135528726Subproblem 2
x + 7 = -11.135528726 Simplifying x + 7 = -11.135528726 Reorder the terms: 7 + x = -11.135528726 Solving 7 + x = -11.135528726 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 = -11.135528726 + -7 Combine like terms: 7 + -7 = 0 0 + x = -11.135528726 + -7 x = -11.135528726 + -7 Combine like terms: -11.135528726 + -7 = -18.135528726 x = -18.135528726 Simplifying x = -18.135528726Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.135528726, -18.135528726}
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