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Simplifying (10x) + -1(0.01x2 + 0.4x + 20) = 0 Reorder the terms: (10x) + -1(20 + 0.4x + 0.01x2) = 0 (10x) + (20 * -1 + 0.4x * -1 + 0.01x2 * -1) = 0 (10x) + (-20 + -0.4x + -0.01x2) = 0 Reorder the terms: -20 + (10x) + -0.4x + -0.01x2 = 0 Combine like terms: (10x) + -0.4x = 9.6x -20 + 9.6x + -0.01x2 = 0 Solving -20 + 9.6x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 2000 + -960x + x2 = 0 Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + -960x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + -960x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + -960x + x2 = 0 + -2000 -960x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 -960x + x2 = -2000 The x term is -960x. Take half its coefficient (-480). Square it (230400) and add it to both sides. Add '230400' to each side of the equation. -960x + 230400 + x2 = -2000 + 230400 Reorder the terms: 230400 + -960x + x2 = -2000 + 230400 Combine like terms: -2000 + 230400 = 228400 230400 + -960x + x2 = 228400 Factor a perfect square on the left side: (x + -480)(x + -480) = 228400 Calculate the square root of the right side: 477.912125814 Break this problem into two subproblems by setting (x + -480) equal to 477.912125814 and -477.912125814.Subproblem 1
x + -480 = 477.912125814 Simplifying x + -480 = 477.912125814 Reorder the terms: -480 + x = 477.912125814 Solving -480 + x = 477.912125814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '480' to each side of the equation. -480 + 480 + x = 477.912125814 + 480 Combine like terms: -480 + 480 = 0 0 + x = 477.912125814 + 480 x = 477.912125814 + 480 Combine like terms: 477.912125814 + 480 = 957.912125814 x = 957.912125814 Simplifying x = 957.912125814Subproblem 2
x + -480 = -477.912125814 Simplifying x + -480 = -477.912125814 Reorder the terms: -480 + x = -477.912125814 Solving -480 + x = -477.912125814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '480' to each side of the equation. -480 + 480 + x = -477.912125814 + 480 Combine like terms: -480 + 480 = 0 0 + x = -477.912125814 + 480 x = -477.912125814 + 480 Combine like terms: -477.912125814 + 480 = 2.087874186 x = 2.087874186 Simplifying x = 2.087874186Solution
The solution to the problem is based on the solutions from the subproblems. x = {957.912125814, 2.087874186}
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