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Simplifying 9 = 0.005x2 + 0.002x Reorder the terms: 9 = 0.002x + 0.005x2 Solving 9 = 0.002x + 0.005x2 Solving for variable 'x'. Reorder the terms: 9 + -0.002x + -0.005x2 = 0.002x + -0.002x + 0.005x2 + -0.005x2 Combine like terms: 0.002x + -0.002x = 0.000 9 + -0.002x + -0.005x2 = 0.000 + 0.005x2 + -0.005x2 9 + -0.002x + -0.005x2 = 0.005x2 + -0.005x2 Combine like terms: 0.005x2 + -0.005x2 = 0.000 9 + -0.002x + -0.005x2 = 0.000 Begin completing the square. Divide all terms by -0.005 the coefficient of the squared term: Divide each side by '-0.005'. -1800 + 0.4x + x2 = 0 Move the constant term to the right: Add '1800' to each side of the equation. -1800 + 0.4x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + 0.4x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + 0.4x + x2 = 0 + 1800 0.4x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 0.4x + x2 = 1800 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 1800 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 1800 + 0.04 Combine like terms: 1800 + 0.04 = 1800.04 0.04 + 0.4x + x2 = 1800.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 1800.04 Calculate the square root of the right side: 42.426878273 Break this problem into two subproblems by setting (x + 0.2) equal to 42.426878273 and -42.426878273.Subproblem 1
x + 0.2 = 42.426878273 Simplifying x + 0.2 = 42.426878273 Reorder the terms: 0.2 + x = 42.426878273 Solving 0.2 + x = 42.426878273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 42.426878273 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 42.426878273 + -0.2 x = 42.426878273 + -0.2 Combine like terms: 42.426878273 + -0.2 = 42.226878273 x = 42.226878273 Simplifying x = 42.226878273Subproblem 2
x + 0.2 = -42.426878273 Simplifying x + 0.2 = -42.426878273 Reorder the terms: 0.2 + x = -42.426878273 Solving 0.2 + x = -42.426878273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -42.426878273 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -42.426878273 + -0.2 x = -42.426878273 + -0.2 Combine like terms: -42.426878273 + -0.2 = -42.626878273 x = -42.626878273 Simplifying x = -42.626878273Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.226878273, -42.626878273}
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