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Simplifying 4x(10 + -1x) = 2 (10 * 4x + -1x * 4x) = 2 (40x + -4x2) = 2 Solving 40x + -4x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 40x + -4x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 40x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 20x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 20x + -2x2)' equal to zero and attempt to solve: Simplifying -1 + 20x + -2x2 = 0 Solving -1 + 20x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -10x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -10x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -10x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -10x + x2 = 0 + -0.5 -10x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -10x + x2 = -0.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -0.5 + 25 Reorder the terms: 25 + -10x + x2 = -0.5 + 25 Combine like terms: -0.5 + 25 = 24.5 25 + -10x + x2 = 24.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 24.5 Calculate the square root of the right side: 4.949747468 Break this problem into two subproblems by setting (x + -5) equal to 4.949747468 and -4.949747468.Subproblem 1
x + -5 = 4.949747468 Simplifying x + -5 = 4.949747468 Reorder the terms: -5 + x = 4.949747468 Solving -5 + x = 4.949747468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.949747468 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.949747468 + 5 x = 4.949747468 + 5 Combine like terms: 4.949747468 + 5 = 9.949747468 x = 9.949747468 Simplifying x = 9.949747468Subproblem 2
x + -5 = -4.949747468 Simplifying x + -5 = -4.949747468 Reorder the terms: -5 + x = -4.949747468 Solving -5 + x = -4.949747468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.949747468 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.949747468 + 5 x = -4.949747468 + 5 Combine like terms: -4.949747468 + 5 = 0.050252532 x = 0.050252532 Simplifying x = 0.050252532Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.949747468, 0.050252532}Solution
x = {9.949747468, 0.050252532}
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