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Simplifying 10x(4 + -10x) + 9 = 1 (4 * 10x + -10x * 10x) + 9 = 1 (40x + -100x2) + 9 = 1 Reorder the terms: 9 + 40x + -100x2 = 1 Solving 9 + 40x + -100x2 = 1 Solving for variable 'x'. Reorder the terms: 9 + -1 + 40x + -100x2 = 1 + -1 Combine like terms: 9 + -1 = 8 8 + 40x + -100x2 = 1 + -1 Combine like terms: 1 + -1 = 0 8 + 40x + -100x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + 10x + -25x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + 10x + -25x2)' equal to zero and attempt to solve: Simplifying 2 + 10x + -25x2 = 0 Solving 2 + 10x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.08 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + -0.4x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + -0.4x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + -0.4x + x2 = 0 + 0.08 -0.4x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 -0.4x + x2 = 0.08 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 = 0.08 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.08 + 0.04 Combine like terms: 0.08 + 0.04 = 0.12 0.04 + -0.4x + x2 = 0.12 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.12 Calculate the square root of the right side: 0.346410162 Break this problem into two subproblems by setting (x + -0.2) equal to 0.346410162 and -0.346410162.Subproblem 1
x + -0.2 = 0.346410162 Simplifying x + -0.2 = 0.346410162 Reorder the terms: -0.2 + x = 0.346410162 Solving -0.2 + x = 0.346410162 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 = 0.346410162 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.346410162 + 0.2 x = 0.346410162 + 0.2 Combine like terms: 0.346410162 + 0.2 = 0.546410162 x = 0.546410162 Simplifying x = 0.546410162Subproblem 2
x + -0.2 = -0.346410162 Simplifying x + -0.2 = -0.346410162 Reorder the terms: -0.2 + x = -0.346410162 Solving -0.2 + x = -0.346410162 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 = -0.346410162 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.346410162 + 0.2 x = -0.346410162 + 0.2 Combine like terms: -0.346410162 + 0.2 = -0.146410162 x = -0.146410162 Simplifying x = -0.146410162Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.546410162, -0.146410162}Solution
x = {0.546410162, -0.146410162}
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