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Simplifying 32x2 + 214x + -3136 = 0 Reorder the terms: -3136 + 214x + 32x2 = 0 Solving -3136 + 214x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1568 + 107x + 16x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1568 + 107x + 16x2)' equal to zero and attempt to solve: Simplifying -1568 + 107x + 16x2 = 0 Solving -1568 + 107x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -98 + 6.6875x + x2 = 0 Move the constant term to the right: Add '98' to each side of the equation. -98 + 6.6875x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 6.6875x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 6.6875x + x2 = 0 + 98 6.6875x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 6.6875x + x2 = 98 The x term is 6.6875x. Take half its coefficient (3.34375). Square it (11.18066406) and add it to both sides. Add '11.18066406' to each side of the equation. 6.6875x + 11.18066406 + x2 = 98 + 11.18066406 Reorder the terms: 11.18066406 + 6.6875x + x2 = 98 + 11.18066406 Combine like terms: 98 + 11.18066406 = 109.18066406 11.18066406 + 6.6875x + x2 = 109.18066406 Factor a perfect square on the left side: (x + 3.34375)(x + 3.34375) = 109.18066406 Calculate the square root of the right side: 10.448955166 Break this problem into two subproblems by setting (x + 3.34375) equal to 10.448955166 and -10.448955166.Subproblem 1
x + 3.34375 = 10.448955166 Simplifying x + 3.34375 = 10.448955166 Reorder the terms: 3.34375 + x = 10.448955166 Solving 3.34375 + x = 10.448955166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.34375' to each side of the equation. 3.34375 + -3.34375 + x = 10.448955166 + -3.34375 Combine like terms: 3.34375 + -3.34375 = 0.00000 0.00000 + x = 10.448955166 + -3.34375 x = 10.448955166 + -3.34375 Combine like terms: 10.448955166 + -3.34375 = 7.105205166 x = 7.105205166 Simplifying x = 7.105205166Subproblem 2
x + 3.34375 = -10.448955166 Simplifying x + 3.34375 = -10.448955166 Reorder the terms: 3.34375 + x = -10.448955166 Solving 3.34375 + x = -10.448955166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.34375' to each side of the equation. 3.34375 + -3.34375 + x = -10.448955166 + -3.34375 Combine like terms: 3.34375 + -3.34375 = 0.00000 0.00000 + x = -10.448955166 + -3.34375 x = -10.448955166 + -3.34375 Combine like terms: -10.448955166 + -3.34375 = -13.792705166 x = -13.792705166 Simplifying x = -13.792705166Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.105205166, -13.792705166}Solution
x = {7.105205166, -13.792705166}
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