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Simplifying 0.8x2 + -12x + 44 = 0 Reorder the terms: 44 + -12x + 0.8x2 = 0 Solving 44 + -12x + 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'. 55 + -15x + x2 = 0 Move the constant term to the right: Add '-55' to each side of the equation. 55 + -15x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + -15x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -15x + x2 = 0 + -55 -15x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 -15x + x2 = -55 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -55 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -55 + 56.25 Combine like terms: -55 + 56.25 = 1.25 56.25 + -15x + x2 = 1.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -7.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -7.5 = 1.118033989 Simplifying x + -7.5 = 1.118033989 Reorder the terms: -7.5 + x = 1.118033989 Solving -7.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 1.118033989 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 1.118033989 + 7.5 x = 1.118033989 + 7.5 Combine like terms: 1.118033989 + 7.5 = 8.618033989 x = 8.618033989 Simplifying x = 8.618033989Subproblem 2
x + -7.5 = -1.118033989 Simplifying x + -7.5 = -1.118033989 Reorder the terms: -7.5 + x = -1.118033989 Solving -7.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -1.118033989 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -1.118033989 + 7.5 x = -1.118033989 + 7.5 Combine like terms: -1.118033989 + 7.5 = 6.381966011 x = 6.381966011 Simplifying x = 6.381966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.618033989, 6.381966011}
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