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Simplifying x2 + x2 + -14x + -49 = 169 Reorder the terms: -49 + -14x + x2 + x2 = 169 Combine like terms: x2 + x2 = 2x2 -49 + -14x + 2x2 = 169 Solving -49 + -14x + 2x2 = 169 Solving for variable 'x'. Reorder the terms: -49 + -169 + -14x + 2x2 = 169 + -169 Combine like terms: -49 + -169 = -218 -218 + -14x + 2x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -218 + -14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-109 + -7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-109 + -7x + x2)' equal to zero and attempt to solve: Simplifying -109 + -7x + x2 = 0 Solving -109 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '109' to each side of the equation. -109 + -7x + 109 + x2 = 0 + 109 Reorder the terms: -109 + 109 + -7x + x2 = 0 + 109 Combine like terms: -109 + 109 = 0 0 + -7x + x2 = 0 + 109 -7x + x2 = 0 + 109 Combine like terms: 0 + 109 = 109 -7x + x2 = 109 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 109 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 109 + 12.25 Combine like terms: 109 + 12.25 = 121.25 12.25 + -7x + x2 = 121.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (x + -3.5) equal to 11.011357773 and -11.011357773.Subproblem 1
x + -3.5 = 11.011357773 Simplifying x + -3.5 = 11.011357773 Reorder the terms: -3.5 + x = 11.011357773 Solving -3.5 + x = 11.011357773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 11.011357773 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 11.011357773 + 3.5 x = 11.011357773 + 3.5 Combine like terms: 11.011357773 + 3.5 = 14.511357773 x = 14.511357773 Simplifying x = 14.511357773Subproblem 2
x + -3.5 = -11.011357773 Simplifying x + -3.5 = -11.011357773 Reorder the terms: -3.5 + x = -11.011357773 Solving -3.5 + x = -11.011357773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -11.011357773 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -11.011357773 + 3.5 x = -11.011357773 + 3.5 Combine like terms: -11.011357773 + 3.5 = -7.511357773 x = -7.511357773 Simplifying x = -7.511357773Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.511357773, -7.511357773}Solution
x = {14.511357773, -7.511357773}
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