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Simplifying 20x2 + 3x + -3 = 0 Reorder the terms: -3 + 3x + 20x2 = 0 Solving -3 + 3x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.15 + 0.15x + x2 = 0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + 0.15x + 0.15 + x2 = 0 + 0.15 Reorder the terms: -0.15 + 0.15 + 0.15x + x2 = 0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + 0.15x + x2 = 0 + 0.15 0.15x + x2 = 0 + 0.15 Combine like terms: 0 + 0.15 = 0.15 0.15x + x2 = 0.15 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = 0.15 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 0.15 + 0.005625 Combine like terms: 0.15 + 0.005625 = 0.155625 0.005625 + 0.15x + x2 = 0.155625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 0.155625 Calculate the square root of the right side: 0.394493346 Break this problem into two subproblems by setting (x + 0.075) equal to 0.394493346 and -0.394493346.Subproblem 1
x + 0.075 = 0.394493346 Simplifying x + 0.075 = 0.394493346 Reorder the terms: 0.075 + x = 0.394493346 Solving 0.075 + x = 0.394493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 0.394493346 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.394493346 + -0.075 x = 0.394493346 + -0.075 Combine like terms: 0.394493346 + -0.075 = 0.319493346 x = 0.319493346 Simplifying x = 0.319493346Subproblem 2
x + 0.075 = -0.394493346 Simplifying x + 0.075 = -0.394493346 Reorder the terms: 0.075 + x = -0.394493346 Solving 0.075 + x = -0.394493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -0.394493346 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.394493346 + -0.075 x = -0.394493346 + -0.075 Combine like terms: -0.394493346 + -0.075 = -0.469493346 x = -0.469493346 Simplifying x = -0.469493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.319493346, -0.469493346}
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