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Simplifying 8x2 + 59x + 2 = 0 Reorder the terms: 2 + 59x + 8x2 = 0 Solving 2 + 59x + 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 + 7.375x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 7.375x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 7.375x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 7.375x + x2 = 0 + -0.25 7.375x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 7.375x + x2 = -0.25 The x term is 7.375x. Take half its coefficient (3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. 7.375x + 13.59765625 + x2 = -0.25 + 13.59765625 Reorder the terms: 13.59765625 + 7.375x + x2 = -0.25 + 13.59765625 Combine like terms: -0.25 + 13.59765625 = 13.34765625 13.59765625 + 7.375x + x2 = 13.34765625 Factor a perfect square on the left side: (x + 3.6875)(x + 3.6875) = 13.34765625 Calculate the square root of the right side: 3.653444436 Break this problem into two subproblems by setting (x + 3.6875) equal to 3.653444436 and -3.653444436.Subproblem 1
x + 3.6875 = 3.653444436 Simplifying x + 3.6875 = 3.653444436 Reorder the terms: 3.6875 + x = 3.653444436 Solving 3.6875 + x = 3.653444436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = 3.653444436 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = 3.653444436 + -3.6875 x = 3.653444436 + -3.6875 Combine like terms: 3.653444436 + -3.6875 = -0.034055564 x = -0.034055564 Simplifying x = -0.034055564Subproblem 2
x + 3.6875 = -3.653444436 Simplifying x + 3.6875 = -3.653444436 Reorder the terms: 3.6875 + x = -3.653444436 Solving 3.6875 + x = -3.653444436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = -3.653444436 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = -3.653444436 + -3.6875 x = -3.653444436 + -3.6875 Combine like terms: -3.653444436 + -3.6875 = -7.340944436 x = -7.340944436 Simplifying x = -7.340944436Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.034055564, -7.340944436}
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