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Simplifying 4x2 + -104x + 168 = 0 Reorder the terms: 168 + -104x + 4x2 = 0 Solving 168 + -104x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(42 + -26x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(42 + -26x + x2)' equal to zero and attempt to solve: Simplifying 42 + -26x + x2 = 0 Solving 42 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -26x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -26x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -26x + x2 = 0 + -42 -26x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -26x + x2 = -42 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -42 + 169 Reorder the terms: 169 + -26x + x2 = -42 + 169 Combine like terms: -42 + 169 = 127 169 + -26x + x2 = 127 Factor a perfect square on the left side: (x + -13)(x + -13) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (x + -13) equal to 11.26942767 and -11.26942767.Subproblem 1
x + -13 = 11.26942767 Simplifying x + -13 = 11.26942767 Reorder the terms: -13 + x = 11.26942767 Solving -13 + x = 11.26942767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 11.26942767 + 13 Combine like terms: -13 + 13 = 0 0 + x = 11.26942767 + 13 x = 11.26942767 + 13 Combine like terms: 11.26942767 + 13 = 24.26942767 x = 24.26942767 Simplifying x = 24.26942767Subproblem 2
x + -13 = -11.26942767 Simplifying x + -13 = -11.26942767 Reorder the terms: -13 + x = -11.26942767 Solving -13 + x = -11.26942767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -11.26942767 + 13 Combine like terms: -13 + 13 = 0 0 + x = -11.26942767 + 13 x = -11.26942767 + 13 Combine like terms: -11.26942767 + 13 = 1.73057233 x = 1.73057233 Simplifying x = 1.73057233Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.26942767, 1.73057233}Solution
x = {24.26942767, 1.73057233}
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