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Simplifying x2 + 14x = 4 Reorder the terms: 14x + x2 = 4 Solving 14x + x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 14x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 14x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 14x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 14x + x2 = 0 + 4 14x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 14x + x2 = 4 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 = 4 + 49 Reorder the terms: 49 + 14x + x2 = 4 + 49 Combine like terms: 4 + 49 = 53 49 + 14x + x2 = 53 Factor a perfect square on the left side: (x + 7)(x + 7) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + 7) equal to 7.280109889 and -7.280109889.Subproblem 1
x + 7 = 7.280109889 Simplifying x + 7 = 7.280109889 Reorder the terms: 7 + x = 7.280109889 Solving 7 + x = 7.280109889 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 = 7.280109889 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.280109889 + -7 x = 7.280109889 + -7 Combine like terms: 7.280109889 + -7 = 0.280109889 x = 0.280109889 Simplifying x = 0.280109889Subproblem 2
x + 7 = -7.280109889 Simplifying x + 7 = -7.280109889 Reorder the terms: 7 + x = -7.280109889 Solving 7 + x = -7.280109889 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 = -7.280109889 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.280109889 + -7 x = -7.280109889 + -7 Combine like terms: -7.280109889 + -7 = -14.280109889 x = -14.280109889 Simplifying x = -14.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.280109889, -14.280109889}
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