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Simplifying 2x2 + 2 = 14x Reorder the terms: 2 + 2x2 = 14x Solving 2 + 2x2 = 14x Solving for variable 'x'. Reorder the terms: 2 + -14x + 2x2 = 14x + -14x Combine like terms: 14x + -14x = 0 2 + -14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -7x + x2)' equal to zero and attempt to solve: Simplifying 1 + -7x + x2 = 0 Solving 1 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -7x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -7x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x + x2 = 0 + -1 -7x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -7x + x2 = -1 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 = -1 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + -7x + x2 = 11.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -3.5 = 3.354101966 Simplifying x + -3.5 = 3.354101966 Reorder the terms: -3.5 + x = 3.354101966 Solving -3.5 + x = 3.354101966 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 = 3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.354101966 + 3.5 x = 3.354101966 + 3.5 Combine like terms: 3.354101966 + 3.5 = 6.854101966 x = 6.854101966 Simplifying x = 6.854101966Subproblem 2
x + -3.5 = -3.354101966 Simplifying x + -3.5 = -3.354101966 Reorder the terms: -3.5 + x = -3.354101966 Solving -3.5 + x = -3.354101966 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 = -3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.354101966 + 3.5 x = -3.354101966 + 3.5 Combine like terms: -3.354101966 + 3.5 = 0.145898034 x = 0.145898034 Simplifying x = 0.145898034Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.854101966, 0.145898034}Solution
x = {6.854101966, 0.145898034}
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