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Simplifying 8x2 + 35x + -2 = 0 Reorder the terms: -2 + 35x + 8x2 = 0 Solving -2 + 35x + 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'. -0.25 + 4.375x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 4.375x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 4.375x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 4.375x + x2 = 0 + 0.25 4.375x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 4.375x + x2 = 0.25 The x term is 4.375x. Take half its coefficient (2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. 4.375x + 4.78515625 + x2 = 0.25 + 4.78515625 Reorder the terms: 4.78515625 + 4.375x + x2 = 0.25 + 4.78515625 Combine like terms: 0.25 + 4.78515625 = 5.03515625 4.78515625 + 4.375x + x2 = 5.03515625 Factor a perfect square on the left side: (x + 2.1875)(x + 2.1875) = 5.03515625 Calculate the square root of the right side: 2.243915384 Break this problem into two subproblems by setting (x + 2.1875) equal to 2.243915384 and -2.243915384.Subproblem 1
x + 2.1875 = 2.243915384 Simplifying x + 2.1875 = 2.243915384 Reorder the terms: 2.1875 + x = 2.243915384 Solving 2.1875 + x = 2.243915384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + x = 2.243915384 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + x = 2.243915384 + -2.1875 x = 2.243915384 + -2.1875 Combine like terms: 2.243915384 + -2.1875 = 0.056415384 x = 0.056415384 Simplifying x = 0.056415384Subproblem 2
x + 2.1875 = -2.243915384 Simplifying x + 2.1875 = -2.243915384 Reorder the terms: 2.1875 + x = -2.243915384 Solving 2.1875 + x = -2.243915384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + x = -2.243915384 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + x = -2.243915384 + -2.1875 x = -2.243915384 + -2.1875 Combine like terms: -2.243915384 + -2.1875 = -4.431415384 x = -4.431415384 Simplifying x = -4.431415384Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.056415384, -4.431415384}
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