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Simplifying -2x2 = 100x + 40 Reorder the terms: -2x2 = 40 + 100x Solving -2x2 = 40 + 100x Solving for variable 'x'. Reorder the terms: -40 + -100x + -2x2 = 40 + 100x + -40 + -100x Reorder the terms: -40 + -100x + -2x2 = 40 + -40 + 100x + -100x Combine like terms: 40 + -40 = 0 -40 + -100x + -2x2 = 0 + 100x + -100x -40 + -100x + -2x2 = 100x + -100x Combine like terms: 100x + -100x = 0 -40 + -100x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(20 + 50x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(20 + 50x + x2)' equal to zero and attempt to solve: Simplifying 20 + 50x + x2 = 0 Solving 20 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 50x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 50x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 50x + x2 = 0 + -20 50x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 50x + x2 = -20 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = -20 + 625 Reorder the terms: 625 + 50x + x2 = -20 + 625 Combine like terms: -20 + 625 = 605 625 + 50x + x2 = 605 Factor a perfect square on the left side: (x + 25)(x + 25) = 605 Calculate the square root of the right side: 24.596747752 Break this problem into two subproblems by setting (x + 25) equal to 24.596747752 and -24.596747752.Subproblem 1
x + 25 = 24.596747752 Simplifying x + 25 = 24.596747752 Reorder the terms: 25 + x = 24.596747752 Solving 25 + x = 24.596747752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 24.596747752 + -25 Combine like terms: 25 + -25 = 0 0 + x = 24.596747752 + -25 x = 24.596747752 + -25 Combine like terms: 24.596747752 + -25 = -0.403252248 x = -0.403252248 Simplifying x = -0.403252248Subproblem 2
x + 25 = -24.596747752 Simplifying x + 25 = -24.596747752 Reorder the terms: 25 + x = -24.596747752 Solving 25 + x = -24.596747752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -24.596747752 + -25 Combine like terms: 25 + -25 = 0 0 + x = -24.596747752 + -25 x = -24.596747752 + -25 Combine like terms: -24.596747752 + -25 = -49.596747752 x = -49.596747752 Simplifying x = -49.596747752Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.403252248, -49.596747752}Solution
x = {-0.403252248, -49.596747752}
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