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Simplifying 400x2 + 4x + -9 = 0 Reorder the terms: -9 + 4x + 400x2 = 0 Solving -9 + 4x + 400x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 400 the coefficient of the squared term: Divide each side by '400'. -0.0225 + 0.01x + x2 = 0 Move the constant term to the right: Add '0.0225' to each side of the equation. -0.0225 + 0.01x + 0.0225 + x2 = 0 + 0.0225 Reorder the terms: -0.0225 + 0.0225 + 0.01x + x2 = 0 + 0.0225 Combine like terms: -0.0225 + 0.0225 = 0.0000 0.0000 + 0.01x + x2 = 0 + 0.0225 0.01x + x2 = 0 + 0.0225 Combine like terms: 0 + 0.0225 = 0.0225 0.01x + x2 = 0.0225 The x term is 0.01x. Take half its coefficient (0.005). Square it (0.000025) and add it to both sides. Add '0.000025' to each side of the equation. 0.01x + 0.000025 + x2 = 0.0225 + 0.000025 Reorder the terms: 0.000025 + 0.01x + x2 = 0.0225 + 0.000025 Combine like terms: 0.0225 + 0.000025 = 0.022525 0.000025 + 0.01x + x2 = 0.022525 Factor a perfect square on the left side: (x + 0.005)(x + 0.005) = 0.022525 Calculate the square root of the right side: 0.15008331 Break this problem into two subproblems by setting (x + 0.005) equal to 0.15008331 and -0.15008331.Subproblem 1
x + 0.005 = 0.15008331 Simplifying x + 0.005 = 0.15008331 Reorder the terms: 0.005 + x = 0.15008331 Solving 0.005 + x = 0.15008331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.005' to each side of the equation. 0.005 + -0.005 + x = 0.15008331 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + x = 0.15008331 + -0.005 x = 0.15008331 + -0.005 Combine like terms: 0.15008331 + -0.005 = 0.14508331 x = 0.14508331 Simplifying x = 0.14508331Subproblem 2
x + 0.005 = -0.15008331 Simplifying x + 0.005 = -0.15008331 Reorder the terms: 0.005 + x = -0.15008331 Solving 0.005 + x = -0.15008331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.005' to each side of the equation. 0.005 + -0.005 + x = -0.15008331 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + x = -0.15008331 + -0.005 x = -0.15008331 + -0.005 Combine like terms: -0.15008331 + -0.005 = -0.15508331 x = -0.15508331 Simplifying x = -0.15508331Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.14508331, -0.15508331}
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