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Simplifying (5x2) + (100x) = -50 Reorder the terms: (100x) + (5x2) = -50 Solving (100x) + (5x2) = -50 Solving for variable 'x'. Reorder the terms: 50 + (100x) + (5x2) = -50 + 50 Combine like terms: -50 + 50 = 0 50 + (100x) + (5x2) = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(10 + (20x) + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + (20x) + x2)' equal to zero and attempt to solve: Simplifying 10 + (20x) + x2 = 0 Solving 10 + (20x) + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + (20x) + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + (20x) + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + (20x) + x2 = 0 + -10 (20x) + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 (20x) + x2 = -10 The x term is (20x). Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. (20x) + 100 + x2 = -10 + 100 Reorder the terms: 100 + (20x) + x2 = -10 + 100 Combine like terms: -10 + 100 = 90 100 + (20x) + x2 = 90 Factor a perfect square on the left side: (x + 10)(x + 10) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + 10) equal to 9.486832981 and -9.486832981.Subproblem 1
x + 10 = 9.486832981 Simplifying x + 10 = 9.486832981 Reorder the terms: 10 + x = 9.486832981 Solving 10 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 9.486832981 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.486832981 + -10 x = 9.486832981 + -10 Combine like terms: 9.486832981 + -10 = -0.513167019 x = -0.513167019 Simplifying x = -0.513167019Subproblem 2
x + 10 = -9.486832981 Simplifying x + 10 = -9.486832981 Reorder the terms: 10 + x = -9.486832981 Solving 10 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -9.486832981 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.486832981 + -10 x = -9.486832981 + -10 Combine like terms: -9.486832981 + -10 = -19.486832981 x = -19.486832981 Simplifying x = -19.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.513167019, -19.486832981}Solution
x = {-0.513167019, -19.486832981}
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