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Simplifying 350 = 400x + -10x2 Solving 350 = 400x + -10x2 Solving for variable 'x'. Reorder the terms: 350 + -400x + 10x2 = 400x + -400x + -10x2 + 10x2 Combine like terms: 400x + -400x = 0 350 + -400x + 10x2 = 0 + -10x2 + 10x2 350 + -400x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 350 + -400x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(35 + -40x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(35 + -40x + x2)' equal to zero and attempt to solve: Simplifying 35 + -40x + x2 = 0 Solving 35 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -40x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -40x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -40x + x2 = 0 + -35 -40x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -40x + x2 = -35 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -35 + 400 Reorder the terms: 400 + -40x + x2 = -35 + 400 Combine like terms: -35 + 400 = 365 400 + -40x + x2 = 365 Factor a perfect square on the left side: (x + -20)(x + -20) = 365 Calculate the square root of the right side: 19.104973175 Break this problem into two subproblems by setting (x + -20) equal to 19.104973175 and -19.104973175.Subproblem 1
x + -20 = 19.104973175 Simplifying x + -20 = 19.104973175 Reorder the terms: -20 + x = 19.104973175 Solving -20 + x = 19.104973175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.104973175 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.104973175 + 20 x = 19.104973175 + 20 Combine like terms: 19.104973175 + 20 = 39.104973175 x = 39.104973175 Simplifying x = 39.104973175Subproblem 2
x + -20 = -19.104973175 Simplifying x + -20 = -19.104973175 Reorder the terms: -20 + x = -19.104973175 Solving -20 + x = -19.104973175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.104973175 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.104973175 + 20 x = -19.104973175 + 20 Combine like terms: -19.104973175 + 20 = 0.895026825 x = 0.895026825 Simplifying x = 0.895026825Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.104973175, 0.895026825}Solution
x = {39.104973175, 0.895026825}
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