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Simplifying 8x2 + 80x = -5 Reorder the terms: 80x + 8x2 = -5 Solving 80x + 8x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + 80x + 8x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 80x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 10x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 10x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 10x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 10x + x2 = 0 + -0.625 10x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 10x + x2 = -0.625 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -0.625 + 25 Reorder the terms: 25 + 10x + x2 = -0.625 + 25 Combine like terms: -0.625 + 25 = 24.375 25 + 10x + x2 = 24.375 Factor a perfect square on the left side: (x + 5)(x + 5) = 24.375 Calculate the square root of the right side: 4.937104415 Break this problem into two subproblems by setting (x + 5) equal to 4.937104415 and -4.937104415.Subproblem 1
x + 5 = 4.937104415 Simplifying x + 5 = 4.937104415 Reorder the terms: 5 + x = 4.937104415 Solving 5 + x = 4.937104415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.937104415 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.937104415 + -5 x = 4.937104415 + -5 Combine like terms: 4.937104415 + -5 = -0.062895585 x = -0.062895585 Simplifying x = -0.062895585Subproblem 2
x + 5 = -4.937104415 Simplifying x + 5 = -4.937104415 Reorder the terms: 5 + x = -4.937104415 Solving 5 + x = -4.937104415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.937104415 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.937104415 + -5 x = -4.937104415 + -5 Combine like terms: -4.937104415 + -5 = -9.937104415 x = -9.937104415 Simplifying x = -9.937104415Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.062895585, -9.937104415}
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