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Simplifying 0.003x2 + 0.03x + 1.6 + -10 = 0 Reorder the terms: 1.6 + -10 + 0.03x + 0.003x2 = 0 Combine like terms: 1.6 + -10 = -8.4 -8.4 + 0.03x + 0.003x2 = 0 Solving -8.4 + 0.03x + 0.003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.003 the coefficient of the squared term: Divide each side by '0.003'. -2800 + 10x + x2 = 0 Move the constant term to the right: Add '2800' to each side of the equation. -2800 + 10x + 2800 + x2 = 0 + 2800 Reorder the terms: -2800 + 2800 + 10x + x2 = 0 + 2800 Combine like terms: -2800 + 2800 = 0 0 + 10x + x2 = 0 + 2800 10x + x2 = 0 + 2800 Combine like terms: 0 + 2800 = 2800 10x + x2 = 2800 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 = 2800 + 25 Reorder the terms: 25 + 10x + x2 = 2800 + 25 Combine like terms: 2800 + 25 = 2825 25 + 10x + x2 = 2825 Factor a perfect square on the left side: (x + 5)(x + 5) = 2825 Calculate the square root of the right side: 53.150729064 Break this problem into two subproblems by setting (x + 5) equal to 53.150729064 and -53.150729064.Subproblem 1
x + 5 = 53.150729064 Simplifying x + 5 = 53.150729064 Reorder the terms: 5 + x = 53.150729064 Solving 5 + x = 53.150729064 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 = 53.150729064 + -5 Combine like terms: 5 + -5 = 0 0 + x = 53.150729064 + -5 x = 53.150729064 + -5 Combine like terms: 53.150729064 + -5 = 48.150729064 x = 48.150729064 Simplifying x = 48.150729064Subproblem 2
x + 5 = -53.150729064 Simplifying x + 5 = -53.150729064 Reorder the terms: 5 + x = -53.150729064 Solving 5 + x = -53.150729064 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 = -53.150729064 + -5 Combine like terms: 5 + -5 = 0 0 + x = -53.150729064 + -5 x = -53.150729064 + -5 Combine like terms: -53.150729064 + -5 = -58.150729064 x = -58.150729064 Simplifying x = -58.150729064Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.150729064, -58.150729064}
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