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Simplifying 2x2 + -24x + 68 = 0 Reorder the terms: 68 + -24x + 2x2 = 0 Solving 68 + -24x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(34 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(34 + -12x + x2)' equal to zero and attempt to solve: Simplifying 34 + -12x + x2 = 0 Solving 34 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -12x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -12x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -12x + x2 = 0 + -34 -12x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -12x + x2 = -34 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -34 + 36 Reorder the terms: 36 + -12x + x2 = -34 + 36 Combine like terms: -34 + 36 = 2 36 + -12x + x2 = 2 Factor a perfect square on the left side: (x + -6)(x + -6) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -6) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -6 = 1.414213562 Simplifying x + -6 = 1.414213562 Reorder the terms: -6 + x = 1.414213562 Solving -6 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 1.414213562 + 6 Combine like terms: -6 + 6 = 0 0 + x = 1.414213562 + 6 x = 1.414213562 + 6 Combine like terms: 1.414213562 + 6 = 7.414213562 x = 7.414213562 Simplifying x = 7.414213562Subproblem 2
x + -6 = -1.414213562 Simplifying x + -6 = -1.414213562 Reorder the terms: -6 + x = -1.414213562 Solving -6 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -1.414213562 + 6 Combine like terms: -6 + 6 = 0 0 + x = -1.414213562 + 6 x = -1.414213562 + 6 Combine like terms: -1.414213562 + 6 = 4.585786438 x = 4.585786438 Simplifying x = 4.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.414213562, 4.585786438}Solution
x = {7.414213562, 4.585786438}
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