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Simplifying 0.18 = x(x + 1.8) Reorder the terms: 0.18 = x(1.8 + x) 0.18 = (1.8 * x + x * x) 0.18 = (1.8x + x2) Solving 0.18 = 1.8x + x2 Solving for variable 'x'. Reorder the terms: 0.18 + -1.8x + -1x2 = 1.8x + -1.8x + x2 + -1x2 Combine like terms: 1.8x + -1.8x = 0.0 0.18 + -1.8x + -1x2 = 0.0 + x2 + -1x2 0.18 + -1.8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.18 + -1.8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.18 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.18' to each side of the equation. -0.18 + 1.8x + 0.18 + x2 = 0 + 0.18 Reorder the terms: -0.18 + 0.18 + 1.8x + x2 = 0 + 0.18 Combine like terms: -0.18 + 0.18 = 0.00 0.00 + 1.8x + x2 = 0 + 0.18 1.8x + x2 = 0 + 0.18 Combine like terms: 0 + 0.18 = 0.18 1.8x + x2 = 0.18 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.18 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.18 + 0.81 Combine like terms: 0.18 + 0.81 = 0.99 0.81 + 1.8x + x2 = 0.99 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.99 Calculate the square root of the right side: 0.994987437 Break this problem into two subproblems by setting (x + 0.9) equal to 0.994987437 and -0.994987437.Subproblem 1
x + 0.9 = 0.994987437 Simplifying x + 0.9 = 0.994987437 Reorder the terms: 0.9 + x = 0.994987437 Solving 0.9 + x = 0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 0.994987437 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.994987437 + -0.9 x = 0.994987437 + -0.9 Combine like terms: 0.994987437 + -0.9 = 0.094987437 x = 0.094987437 Simplifying x = 0.094987437Subproblem 2
x + 0.9 = -0.994987437 Simplifying x + 0.9 = -0.994987437 Reorder the terms: 0.9 + x = -0.994987437 Solving 0.9 + x = -0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -0.994987437 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.994987437 + -0.9 x = -0.994987437 + -0.9 Combine like terms: -0.994987437 + -0.9 = -1.894987437 x = -1.894987437 Simplifying x = -1.894987437Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.094987437, -1.894987437}
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