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Simplifying 0.009 + -4x2 = 1.6x Solving 0.009 + -4x2 = 1.6x Solving for variable 'x'. Reorder the terms: 0.009 + -1.6x + -4x2 = 1.6x + -1.6x Combine like terms: 1.6x + -1.6x = 0.0 0.009 + -1.6x + -4x2 = 0.0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.00225 + 0.4x + x2 = 0.0 Move the constant term to the right: Add '0.00225' to each side of the equation. -0.00225 + 0.4x + 0.00225 + x2 = 0.0 + 0.00225 Reorder the terms: -0.00225 + 0.00225 + 0.4x + x2 = 0.0 + 0.00225 Combine like terms: -0.00225 + 0.00225 = 0.00000 0.00000 + 0.4x + x2 = 0.0 + 0.00225 0.4x + x2 = 0.0 + 0.00225 Combine like terms: 0.0 + 0.00225 = 0.00225 0.4x + x2 = 0.00225 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 = 0.00225 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.00225 + 0.04 Combine like terms: 0.00225 + 0.04 = 0.04225 0.04 + 0.4x + x2 = 0.04225 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.04225 Calculate the square root of the right side: 0.205548048 Break this problem into two subproblems by setting (x + 0.2) equal to 0.205548048 and -0.205548048.Subproblem 1
x + 0.2 = 0.205548048 Simplifying x + 0.2 = 0.205548048 Reorder the terms: 0.2 + x = 0.205548048 Solving 0.2 + x = 0.205548048 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 = 0.205548048 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.205548048 + -0.2 x = 0.205548048 + -0.2 Combine like terms: 0.205548048 + -0.2 = 0.005548048 x = 0.005548048 Simplifying x = 0.005548048Subproblem 2
x + 0.2 = -0.205548048 Simplifying x + 0.2 = -0.205548048 Reorder the terms: 0.2 + x = -0.205548048 Solving 0.2 + x = -0.205548048 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 = -0.205548048 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.205548048 + -0.2 x = -0.205548048 + -0.2 Combine like terms: -0.205548048 + -0.2 = -0.405548048 x = -0.405548048 Simplifying x = -0.405548048Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.005548048, -0.405548048}
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