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Simplifying 6x2 + 35x = 2x2 + -16 Reorder the terms: 35x + 6x2 = 2x2 + -16 Reorder the terms: 35x + 6x2 = -16 + 2x2 Solving 35x + 6x2 = -16 + 2x2 Solving for variable 'x'. Reorder the terms: 16 + 35x + 6x2 + -2x2 = -16 + 2x2 + 16 + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 16 + 35x + 4x2 = -16 + 2x2 + 16 + -2x2 Reorder the terms: 16 + 35x + 4x2 = -16 + 16 + 2x2 + -2x2 Combine like terms: -16 + 16 = 0 16 + 35x + 4x2 = 0 + 2x2 + -2x2 16 + 35x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 16 + 35x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4 + 8.75x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 8.75x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 8.75x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8.75x + x2 = 0 + -4 8.75x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 8.75x + x2 = -4 The x term is 8.75x. Take half its coefficient (4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. 8.75x + 19.140625 + x2 = -4 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = -4 + 19.140625 Combine like terms: -4 + 19.140625 = 15.140625 19.140625 + 8.75x + x2 = 15.140625 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 15.140625 Calculate the square root of the right side: 3.891095604 Break this problem into two subproblems by setting (x + 4.375) equal to 3.891095604 and -3.891095604.Subproblem 1
x + 4.375 = 3.891095604 Simplifying x + 4.375 = 3.891095604 Reorder the terms: 4.375 + x = 3.891095604 Solving 4.375 + x = 3.891095604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = 3.891095604 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 3.891095604 + -4.375 x = 3.891095604 + -4.375 Combine like terms: 3.891095604 + -4.375 = -0.483904396 x = -0.483904396 Simplifying x = -0.483904396Subproblem 2
x + 4.375 = -3.891095604 Simplifying x + 4.375 = -3.891095604 Reorder the terms: 4.375 + x = -3.891095604 Solving 4.375 + x = -3.891095604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = -3.891095604 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -3.891095604 + -4.375 x = -3.891095604 + -4.375 Combine like terms: -3.891095604 + -4.375 = -8.266095604 x = -8.266095604 Simplifying x = -8.266095604Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.483904396, -8.266095604}
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