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Simplifying 1250x2 + 2500x + 1050 + -2400 = 0 Reorder the terms: 1050 + -2400 + 2500x + 1250x2 = 0 Combine like terms: 1050 + -2400 = -1350 -1350 + 2500x + 1250x2 = 0 Solving -1350 + 2500x + 1250x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50'. 50(-27 + 50x + 25x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-27 + 50x + 25x2)' equal to zero and attempt to solve: Simplifying -27 + 50x + 25x2 = 0 Solving -27 + 50x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.08 + 2x + x2 = 0 Move the constant term to the right: Add '1.08' to each side of the equation. -1.08 + 2x + 1.08 + x2 = 0 + 1.08 Reorder the terms: -1.08 + 1.08 + 2x + x2 = 0 + 1.08 Combine like terms: -1.08 + 1.08 = 0.00 0.00 + 2x + x2 = 0 + 1.08 2x + x2 = 0 + 1.08 Combine like terms: 0 + 1.08 = 1.08 2x + x2 = 1.08 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.08 + 1 Reorder the terms: 1 + 2x + x2 = 1.08 + 1 Combine like terms: 1.08 + 1 = 2.08 1 + 2x + x2 = 2.08 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.08 Calculate the square root of the right side: 1.44222051 Break this problem into two subproblems by setting (x + 1) equal to 1.44222051 and -1.44222051.Subproblem 1
x + 1 = 1.44222051 Simplifying x + 1 = 1.44222051 Reorder the terms: 1 + x = 1.44222051 Solving 1 + x = 1.44222051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.44222051 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.44222051 + -1 x = 1.44222051 + -1 Combine like terms: 1.44222051 + -1 = 0.44222051 x = 0.44222051 Simplifying x = 0.44222051Subproblem 2
x + 1 = -1.44222051 Simplifying x + 1 = -1.44222051 Reorder the terms: 1 + x = -1.44222051 Solving 1 + x = -1.44222051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.44222051 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.44222051 + -1 x = -1.44222051 + -1 Combine like terms: -1.44222051 + -1 = -2.44222051 x = -2.44222051 Simplifying x = -2.44222051Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.44222051, -2.44222051}Solution
x = {0.44222051, -2.44222051}
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