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Simplifying x2 + -14x + -49 = 4 Reorder the terms: -49 + -14x + x2 = 4 Solving -49 + -14x + x2 = 4 Solving for variable 'x'. Reorder the terms: -49 + -4 + -14x + x2 = 4 + -4 Combine like terms: -49 + -4 = -53 -53 + -14x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -53 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -14x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + -14x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -14x + x2 = 0 + 53 -14x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 -14x + x2 = 53 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 = 53 + 49 Reorder the terms: 49 + -14x + x2 = 53 + 49 Combine like terms: 53 + 49 = 102 49 + -14x + x2 = 102 Factor a perfect square on the left side: (x + -7)(x + -7) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (x + -7) equal to 10.099504938 and -10.099504938.Subproblem 1
x + -7 = 10.099504938 Simplifying x + -7 = 10.099504938 Reorder the terms: -7 + x = 10.099504938 Solving -7 + x = 10.099504938 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 = 10.099504938 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.099504938 + 7 x = 10.099504938 + 7 Combine like terms: 10.099504938 + 7 = 17.099504938 x = 17.099504938 Simplifying x = 17.099504938Subproblem 2
x + -7 = -10.099504938 Simplifying x + -7 = -10.099504938 Reorder the terms: -7 + x = -10.099504938 Solving -7 + x = -10.099504938 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 = -10.099504938 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.099504938 + 7 x = -10.099504938 + 7 Combine like terms: -10.099504938 + 7 = -3.099504938 x = -3.099504938 Simplifying x = -3.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.099504938, -3.099504938}
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