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Simplifying x2 + -14x + 49 = 53 Reorder the terms: 49 + -14x + x2 = 53 Solving 49 + -14x + x2 = 53 Solving for variable 'x'. Reorder the terms: 49 + -53 + -14x + x2 = 53 + -53 Combine like terms: 49 + -53 = -4 -4 + -14x + x2 = 53 + -53 Combine like terms: 53 + -53 = 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 = 14.280109889 x = 14.280109889 Simplifying x = 14.280109889Subproblem 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 = -0.280109889 x = -0.280109889 Simplifying x = -0.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.280109889, -0.280109889}
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