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Simplifying 0.8x2 + 8x + 19 = 0 Reorder the terms: 19 + 8x + 0.8x2 = 0 Solving 19 + 8x + 0.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 23.75 + 10x + x2 = 0 Move the constant term to the right: Add '-23.75' to each side of the equation. 23.75 + 10x + -23.75 + x2 = 0 + -23.75 Reorder the terms: 23.75 + -23.75 + 10x + x2 = 0 + -23.75 Combine like terms: 23.75 + -23.75 = 0.00 0.00 + 10x + x2 = 0 + -23.75 10x + x2 = 0 + -23.75 Combine like terms: 0 + -23.75 = -23.75 10x + x2 = -23.75 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 = -23.75 + 25 Reorder the terms: 25 + 10x + x2 = -23.75 + 25 Combine like terms: -23.75 + 25 = 1.25 25 + 10x + x2 = 1.25 Factor a perfect square on the left side: (x + 5)(x + 5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 5 = 1.118033989 Simplifying x + 5 = 1.118033989 Reorder the terms: 5 + x = 1.118033989 Solving 5 + x = 1.118033989 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 = 1.118033989 + -5 Combine like terms: 5 + -5 = 0 0 + x = 1.118033989 + -5 x = 1.118033989 + -5 Combine like terms: 1.118033989 + -5 = -3.881966011 x = -3.881966011 Simplifying x = -3.881966011Subproblem 2
x + 5 = -1.118033989 Simplifying x + 5 = -1.118033989 Reorder the terms: 5 + x = -1.118033989 Solving 5 + x = -1.118033989 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 = -1.118033989 + -5 Combine like terms: 5 + -5 = 0 0 + x = -1.118033989 + -5 x = -1.118033989 + -5 Combine like terms: -1.118033989 + -5 = -6.118033989 x = -6.118033989 Simplifying x = -6.118033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.881966011, -6.118033989}
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