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Simplifying 16x2 + -34x + -336 = 0 Reorder the terms: -336 + -34x + 16x2 = 0 Solving -336 + -34x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-168 + -17x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-168 + -17x + 8x2)' equal to zero and attempt to solve: Simplifying -168 + -17x + 8x2 = 0 Solving -168 + -17x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -21 + -2.125x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -2.125x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -2.125x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2.125x + x2 = 0 + 21 -2.125x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2.125x + x2 = 21 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = 21 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = 21 + 1.12890625 Combine like terms: 21 + 1.12890625 = 22.12890625 1.12890625 + -2.125x + x2 = 22.12890625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 22.12890625 Calculate the square root of the right side: 4.704137142 Break this problem into two subproblems by setting (x + -1.0625) equal to 4.704137142 and -4.704137142.Subproblem 1
x + -1.0625 = 4.704137142 Simplifying x + -1.0625 = 4.704137142 Reorder the terms: -1.0625 + x = 4.704137142 Solving -1.0625 + x = 4.704137142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 4.704137142 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 4.704137142 + 1.0625 x = 4.704137142 + 1.0625 Combine like terms: 4.704137142 + 1.0625 = 5.766637142 x = 5.766637142 Simplifying x = 5.766637142Subproblem 2
x + -1.0625 = -4.704137142 Simplifying x + -1.0625 = -4.704137142 Reorder the terms: -1.0625 + x = -4.704137142 Solving -1.0625 + x = -4.704137142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -4.704137142 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -4.704137142 + 1.0625 x = -4.704137142 + 1.0625 Combine like terms: -4.704137142 + 1.0625 = -3.641637142 x = -3.641637142 Simplifying x = -3.641637142Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.766637142, -3.641637142}Solution
x = {5.766637142, -3.641637142}
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