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Simplifying 8x2 + 8x + -7921 = 0 Reorder the terms: -7921 + 8x + 8x2 = 0 Solving -7921 + 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'. -990.125 + x + x2 = 0 Move the constant term to the right: Add '990.125' to each side of the equation. -990.125 + x + 990.125 + x2 = 0 + 990.125 Reorder the terms: -990.125 + 990.125 + x + x2 = 0 + 990.125 Combine like terms: -990.125 + 990.125 = 0.000 0.000 + x + x2 = 0 + 990.125 x + x2 = 0 + 990.125 Combine like terms: 0 + 990.125 = 990.125 x + x2 = 990.125 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 = 990.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 990.125 + 0.25 Combine like terms: 990.125 + 0.25 = 990.375 1.25 + x2 = 990.375 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 990.375 Calculate the square root of the right side: 31.470224022 Break this problem into two subproblems by setting (x + 0.5) equal to 31.470224022 and -31.470224022.Subproblem 1
x + 0.5 = 31.470224022 Simplifying x + 0.5 = 31.470224022 Reorder the terms: 0.5 + x = 31.470224022 Solving 0.5 + x = 31.470224022 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 = 31.470224022 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 31.470224022 + -0.5 x = 31.470224022 + -0.5 Combine like terms: 31.470224022 + -0.5 = 30.970224022 x = 30.970224022 Simplifying x = 30.970224022Subproblem 2
x + 0.5 = -31.470224022 Simplifying x + 0.5 = -31.470224022 Reorder the terms: 0.5 + x = -31.470224022 Solving 0.5 + x = -31.470224022 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 = -31.470224022 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -31.470224022 + -0.5 x = -31.470224022 + -0.5 Combine like terms: -31.470224022 + -0.5 = -31.970224022 x = -31.970224022 Simplifying x = -31.970224022Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.970224022, -31.970224022}
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