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Simplifying 8x2 + -35x + -4 = 0 Reorder the terms: -4 + -35x + 8x2 = 0 Solving -4 + -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'. -0.5 + -4.375x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -4.375x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -4.375x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -4.375x + x2 = 0 + 0.5 -4.375x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -4.375x + x2 = 0.5 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 = 0.5 + 4.78515625 Reorder the terms: 4.78515625 + -4.375x + x2 = 0.5 + 4.78515625 Combine like terms: 0.5 + 4.78515625 = 5.28515625 4.78515625 + -4.375x + x2 = 5.28515625 Factor a perfect square on the left side: (x + -2.1875)(x + -2.1875) = 5.28515625 Calculate the square root of the right side: 2.29894677 Break this problem into two subproblems by setting (x + -2.1875) equal to 2.29894677 and -2.29894677.Subproblem 1
x + -2.1875 = 2.29894677 Simplifying x + -2.1875 = 2.29894677 Reorder the terms: -2.1875 + x = 2.29894677 Solving -2.1875 + x = 2.29894677 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 = 2.29894677 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = 2.29894677 + 2.1875 x = 2.29894677 + 2.1875 Combine like terms: 2.29894677 + 2.1875 = 4.48644677 x = 4.48644677 Simplifying x = 4.48644677Subproblem 2
x + -2.1875 = -2.29894677 Simplifying x + -2.1875 = -2.29894677 Reorder the terms: -2.1875 + x = -2.29894677 Solving -2.1875 + x = -2.29894677 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 = -2.29894677 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = -2.29894677 + 2.1875 x = -2.29894677 + 2.1875 Combine like terms: -2.29894677 + 2.1875 = -0.11144677 x = -0.11144677 Simplifying x = -0.11144677Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.48644677, -0.11144677}
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