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Simplifying x2 + x2 = 100x + -100 Combine like terms: x2 + x2 = 2x2 2x2 = 100x + -100 Reorder the terms: 2x2 = -100 + 100x Solving 2x2 = -100 + 100x Solving for variable 'x'. Reorder the terms: 100 + -100x + 2x2 = -100 + 100x + 100 + -100x Reorder the terms: 100 + -100x + 2x2 = -100 + 100 + 100x + -100x Combine like terms: -100 + 100 = 0 100 + -100x + 2x2 = 0 + 100x + -100x 100 + -100x + 2x2 = 100x + -100x Combine like terms: 100x + -100x = 0 100 + -100x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -50x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -50x + x2)' equal to zero and attempt to solve: Simplifying 50 + -50x + x2 = 0 Solving 50 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -50x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -50x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -50x + x2 = 0 + -50 -50x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -50x + x2 = -50 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 = -50 + 625 Reorder the terms: 625 + -50x + x2 = -50 + 625 Combine like terms: -50 + 625 = 575 625 + -50x + x2 = 575 Factor a perfect square on the left side: (x + -25)(x + -25) = 575 Calculate the square root of the right side: 23.979157617 Break this problem into two subproblems by setting (x + -25) equal to 23.979157617 and -23.979157617.Subproblem 1
x + -25 = 23.979157617 Simplifying x + -25 = 23.979157617 Reorder the terms: -25 + x = 23.979157617 Solving -25 + x = 23.979157617 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 = 23.979157617 + 25 Combine like terms: -25 + 25 = 0 0 + x = 23.979157617 + 25 x = 23.979157617 + 25 Combine like terms: 23.979157617 + 25 = 48.979157617 x = 48.979157617 Simplifying x = 48.979157617Subproblem 2
x + -25 = -23.979157617 Simplifying x + -25 = -23.979157617 Reorder the terms: -25 + x = -23.979157617 Solving -25 + x = -23.979157617 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 = -23.979157617 + 25 Combine like terms: -25 + 25 = 0 0 + x = -23.979157617 + 25 x = -23.979157617 + 25 Combine like terms: -23.979157617 + 25 = 1.020842383 x = 1.020842383 Simplifying x = 1.020842383Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.979157617, 1.020842383}Solution
x = {48.979157617, 1.020842383}
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