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Simplifying -16x2 + 357x + 107 = 0 Reorder the terms: 107 + 357x + -16x2 = 0 Solving 107 + 357x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -6.6875 + -22.3125x + x2 = 0 Move the constant term to the right: Add '6.6875' to each side of the equation. -6.6875 + -22.3125x + 6.6875 + x2 = 0 + 6.6875 Reorder the terms: -6.6875 + 6.6875 + -22.3125x + x2 = 0 + 6.6875 Combine like terms: -6.6875 + 6.6875 = 0.0000 0.0000 + -22.3125x + x2 = 0 + 6.6875 -22.3125x + x2 = 0 + 6.6875 Combine like terms: 0 + 6.6875 = 6.6875 -22.3125x + x2 = 6.6875 The x term is -22.3125x. Take half its coefficient (-11.15625). Square it (124.4619141) and add it to both sides. Add '124.4619141' to each side of the equation. -22.3125x + 124.4619141 + x2 = 6.6875 + 124.4619141 Reorder the terms: 124.4619141 + -22.3125x + x2 = 6.6875 + 124.4619141 Combine like terms: 6.6875 + 124.4619141 = 131.1494141 124.4619141 + -22.3125x + x2 = 131.1494141 Factor a perfect square on the left side: (x + -11.15625)(x + -11.15625) = 131.1494141 Calculate the square root of the right side: 11.452048467 Break this problem into two subproblems by setting (x + -11.15625) equal to 11.452048467 and -11.452048467.Subproblem 1
x + -11.15625 = 11.452048467 Simplifying x + -11.15625 = 11.452048467 Reorder the terms: -11.15625 + x = 11.452048467 Solving -11.15625 + x = 11.452048467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.15625' to each side of the equation. -11.15625 + 11.15625 + x = 11.452048467 + 11.15625 Combine like terms: -11.15625 + 11.15625 = 0.00000 0.00000 + x = 11.452048467 + 11.15625 x = 11.452048467 + 11.15625 Combine like terms: 11.452048467 + 11.15625 = 22.608298467 x = 22.608298467 Simplifying x = 22.608298467Subproblem 2
x + -11.15625 = -11.452048467 Simplifying x + -11.15625 = -11.452048467 Reorder the terms: -11.15625 + x = -11.452048467 Solving -11.15625 + x = -11.452048467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.15625' to each side of the equation. -11.15625 + 11.15625 + x = -11.452048467 + 11.15625 Combine like terms: -11.15625 + 11.15625 = 0.00000 0.00000 + x = -11.452048467 + 11.15625 x = -11.452048467 + 11.15625 Combine like terms: -11.452048467 + 11.15625 = -0.295798467 x = -0.295798467 Simplifying x = -0.295798467Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.608298467, -0.295798467}
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