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Simplifying 8x2 + 4x + -35 = 0 Reorder the terms: -35 + 4x + 8x2 = 0 Solving -35 + 4x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + 0.5x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 0.5x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 0.5x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 0.5x + x2 = 0 + 4.375 0.5x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 0.5x + x2 = 4.375 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 4.375 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 4.375 + 0.0625 Combine like terms: 4.375 + 0.0625 = 4.4375 0.0625 + 0.5x + x2 = 4.4375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 4.4375 Calculate the square root of the right side: 2.106537443 Break this problem into two subproblems by setting (x + 0.25) equal to 2.106537443 and -2.106537443.Subproblem 1
x + 0.25 = 2.106537443 Simplifying x + 0.25 = 2.106537443 Reorder the terms: 0.25 + x = 2.106537443 Solving 0.25 + x = 2.106537443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.106537443 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.106537443 + -0.25 x = 2.106537443 + -0.25 Combine like terms: 2.106537443 + -0.25 = 1.856537443 x = 1.856537443 Simplifying x = 1.856537443Subproblem 2
x + 0.25 = -2.106537443 Simplifying x + 0.25 = -2.106537443 Reorder the terms: 0.25 + x = -2.106537443 Solving 0.25 + x = -2.106537443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.106537443 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.106537443 + -0.25 x = -2.106537443 + -0.25 Combine like terms: -2.106537443 + -0.25 = -2.356537443 x = -2.356537443 Simplifying x = -2.356537443Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.856537443, -2.356537443}
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