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Simplifying x2 + -71 = 14x Reorder the terms: -71 + x2 = 14x Solving -71 + x2 = 14x Solving for variable 'x'. Reorder the terms: -71 + -14x + x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -71 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -14x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + -14x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -14x + x2 = 0 + 71 -14x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 -14x + x2 = 71 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 = 71 + 49 Reorder the terms: 49 + -14x + x2 = 71 + 49 Combine like terms: 71 + 49 = 120 49 + -14x + x2 = 120 Factor a perfect square on the left side: (x + -7)(x + -7) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + -7) equal to 10.95445115 and -10.95445115.Subproblem 1
x + -7 = 10.95445115 Simplifying x + -7 = 10.95445115 Reorder the terms: -7 + x = 10.95445115 Solving -7 + x = 10.95445115 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 = 10.95445115 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.95445115 + 7 x = 10.95445115 + 7 Combine like terms: 10.95445115 + 7 = 17.95445115 x = 17.95445115 Simplifying x = 17.95445115Subproblem 2
x + -7 = -10.95445115 Simplifying x + -7 = -10.95445115 Reorder the terms: -7 + x = -10.95445115 Solving -7 + x = -10.95445115 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 = -10.95445115 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.95445115 + 7 x = -10.95445115 + 7 Combine like terms: -10.95445115 + 7 = -3.95445115 x = -3.95445115 Simplifying x = -3.95445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.95445115, -3.95445115}
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