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Simplifying (0.1)(1) + 0x = 0.02x(x + 1) Multiply 0.1 * 1 0.1 + 0x = 0.02x(x + 1) Anything times zero is zero. 0.1 + 0x = 0.02x(x + 1) Combine like terms: 0.1 + 0 = 0.1 0.1 = 0.02x(x + 1) Reorder the terms: 0.1 = 0.02x(1 + x) 0.1 = (1 * 0.02x + x * 0.02x) 0.1 = (0.02x + 0.02x2) Solving 0.1 = 0.02x + 0.02x2 Solving for variable 'x'. Reorder the terms: 0.1 + -0.02x + -0.02x2 = 0.02x + -0.02x + 0.02x2 + -0.02x2 Combine like terms: 0.02x + -0.02x = 0.00 0.1 + -0.02x + -0.02x2 = 0.00 + 0.02x2 + -0.02x2 0.1 + -0.02x + -0.02x2 = 0.02x2 + -0.02x2 Combine like terms: 0.02x2 + -0.02x2 = 0.00 0.1 + -0.02x + -0.02x2 = 0.00 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. -5 + x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x + x2 = 0 + 5 x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 x + x2 = 5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 1.25 + x2 = 5.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 0.5 = 2.291287847 Simplifying x + 0.5 = 2.291287847 Reorder the terms: 0.5 + x = 2.291287847 Solving 0.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.291287847 + -0.5 x = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 x = 1.791287847 Simplifying x = 1.791287847Subproblem 2
x + 0.5 = -2.291287847 Simplifying x + 0.5 = -2.291287847 Reorder the terms: 0.5 + x = -2.291287847 Solving 0.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.291287847 + -0.5 x = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 x = -2.791287847 Simplifying x = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.791287847, -2.791287847}
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