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Simplifying 8x2 + 8x + -83 = 0 Reorder the terms: -83 + 8x + 8x2 = 0 Solving -83 + 8x + 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'. -10.375 + x + x2 = 0 Move the constant term to the right: Add '10.375' to each side of the equation. -10.375 + x + 10.375 + x2 = 0 + 10.375 Reorder the terms: -10.375 + 10.375 + x + x2 = 0 + 10.375 Combine like terms: -10.375 + 10.375 = 0.000 0.000 + x + x2 = 0 + 10.375 x + x2 = 0 + 10.375 Combine like terms: 0 + 10.375 = 10.375 x + x2 = 10.375 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 10.375 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 10.375 + 0.25 Combine like terms: 10.375 + 0.25 = 10.625 1.25 + x2 = 10.625 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 10.625 Calculate the square root of the right side: 3.259601203 Break this problem into two subproblems by setting (x + 0.5) equal to 3.259601203 and -3.259601203.Subproblem 1
x + 0.5 = 3.259601203 Simplifying x + 0.5 = 3.259601203 Reorder the terms: 0.5 + x = 3.259601203 Solving 0.5 + x = 3.259601203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.259601203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.259601203 + -0.5 x = 3.259601203 + -0.5 Combine like terms: 3.259601203 + -0.5 = 2.759601203 x = 2.759601203 Simplifying x = 2.759601203Subproblem 2
x + 0.5 = -3.259601203 Simplifying x + 0.5 = -3.259601203 Reorder the terms: 0.5 + x = -3.259601203 Solving 0.5 + x = -3.259601203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.259601203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.259601203 + -0.5 x = -3.259601203 + -0.5 Combine like terms: -3.259601203 + -0.5 = -3.759601203 x = -3.759601203 Simplifying x = -3.759601203Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.759601203, -3.759601203}
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