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Simplifying 100x + -2x2 = 700 Solving 100x + -2x2 = 700 Solving for variable 'x'. Reorder the terms: -700 + 100x + -2x2 = 700 + -700 Combine like terms: 700 + -700 = 0 -700 + 100x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-350 + 50x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-350 + 50x + -1x2)' equal to zero and attempt to solve: Simplifying -350 + 50x + -1x2 = 0 Solving -350 + 50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 350 + -50x + x2 = 0 Move the constant term to the right: Add '-350' to each side of the equation. 350 + -50x + -350 + x2 = 0 + -350 Reorder the terms: 350 + -350 + -50x + x2 = 0 + -350 Combine like terms: 350 + -350 = 0 0 + -50x + x2 = 0 + -350 -50x + x2 = 0 + -350 Combine like terms: 0 + -350 = -350 -50x + x2 = -350 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 = -350 + 625 Reorder the terms: 625 + -50x + x2 = -350 + 625 Combine like terms: -350 + 625 = 275 625 + -50x + x2 = 275 Factor a perfect square on the left side: (x + -25)(x + -25) = 275 Calculate the square root of the right side: 16.583123952 Break this problem into two subproblems by setting (x + -25) equal to 16.583123952 and -16.583123952.Subproblem 1
x + -25 = 16.583123952 Simplifying x + -25 = 16.583123952 Reorder the terms: -25 + x = 16.583123952 Solving -25 + x = 16.583123952 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 = 16.583123952 + 25 Combine like terms: -25 + 25 = 0 0 + x = 16.583123952 + 25 x = 16.583123952 + 25 Combine like terms: 16.583123952 + 25 = 41.583123952 x = 41.583123952 Simplifying x = 41.583123952Subproblem 2
x + -25 = -16.583123952 Simplifying x + -25 = -16.583123952 Reorder the terms: -25 + x = -16.583123952 Solving -25 + x = -16.583123952 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 = -16.583123952 + 25 Combine like terms: -25 + 25 = 0 0 + x = -16.583123952 + 25 x = -16.583123952 + 25 Combine like terms: -16.583123952 + 25 = 8.416876048 x = 8.416876048 Simplifying x = 8.416876048Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.583123952, 8.416876048}Solution
x = {41.583123952, 8.416876048}
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