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Simplifying x(20x) + (8x + -2) = 5 Remove parenthesis around (20x) x * 20x + (8x + -2) = 5 Reorder the terms for easier multiplication: 20x * x + (8x + -2) = 5 Multiply x * x 20x2 + (8x + -2) = 5 Reorder the terms: 20x2 + (-2 + 8x) = 5 Remove parenthesis around (-2 + 8x) 20x2 + -2 + 8x = 5 Reorder the terms: -2 + 8x + 20x2 = 5 Solving -2 + 8x + 20x2 = 5 Solving for variable 'x'. Reorder the terms: -2 + -5 + 8x + 20x2 = 5 + -5 Combine like terms: -2 + -5 = -7 -7 + 8x + 20x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -7 + 8x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.35 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + 0.4x + 0.35 + x2 = 0 + 0.35 Reorder the terms: -0.35 + 0.35 + 0.4x + x2 = 0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + 0.4x + x2 = 0 + 0.35 0.4x + x2 = 0 + 0.35 Combine like terms: 0 + 0.35 = 0.35 0.4x + x2 = 0.35 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 = 0.35 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.35 + 0.04 Combine like terms: 0.35 + 0.04 = 0.39 0.04 + 0.4x + x2 = 0.39 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.39 Calculate the square root of the right side: 0.6244998 Break this problem into two subproblems by setting (x + 0.2) equal to 0.6244998 and -0.6244998.Subproblem 1
x + 0.2 = 0.6244998 Simplifying x + 0.2 = 0.6244998 Reorder the terms: 0.2 + x = 0.6244998 Solving 0.2 + x = 0.6244998 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 = 0.6244998 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.6244998 + -0.2 x = 0.6244998 + -0.2 Combine like terms: 0.6244998 + -0.2 = 0.4244998 x = 0.4244998 Simplifying x = 0.4244998Subproblem 2
x + 0.2 = -0.6244998 Simplifying x + 0.2 = -0.6244998 Reorder the terms: 0.2 + x = -0.6244998 Solving 0.2 + x = -0.6244998 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 = -0.6244998 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.6244998 + -0.2 x = -0.6244998 + -0.2 Combine like terms: -0.6244998 + -0.2 = -0.8244998 x = -0.8244998 Simplifying x = -0.8244998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4244998, -0.8244998}
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