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Simplifying 2x2 + 56x + -2850 = 0 Reorder the terms: -2850 + 56x + 2x2 = 0 Solving -2850 + 56x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1425 + 28x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1425 + 28x + x2)' equal to zero and attempt to solve: Simplifying -1425 + 28x + x2 = 0 Solving -1425 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1425' to each side of the equation. -1425 + 28x + 1425 + x2 = 0 + 1425 Reorder the terms: -1425 + 1425 + 28x + x2 = 0 + 1425 Combine like terms: -1425 + 1425 = 0 0 + 28x + x2 = 0 + 1425 28x + x2 = 0 + 1425 Combine like terms: 0 + 1425 = 1425 28x + x2 = 1425 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 1425 + 196 Reorder the terms: 196 + 28x + x2 = 1425 + 196 Combine like terms: 1425 + 196 = 1621 196 + 28x + x2 = 1621 Factor a perfect square on the left side: (x + 14)(x + 14) = 1621 Calculate the square root of the right side: 40.261644278 Break this problem into two subproblems by setting (x + 14) equal to 40.261644278 and -40.261644278.Subproblem 1
x + 14 = 40.261644278 Simplifying x + 14 = 40.261644278 Reorder the terms: 14 + x = 40.261644278 Solving 14 + x = 40.261644278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 40.261644278 + -14 Combine like terms: 14 + -14 = 0 0 + x = 40.261644278 + -14 x = 40.261644278 + -14 Combine like terms: 40.261644278 + -14 = 26.261644278 x = 26.261644278 Simplifying x = 26.261644278Subproblem 2
x + 14 = -40.261644278 Simplifying x + 14 = -40.261644278 Reorder the terms: 14 + x = -40.261644278 Solving 14 + x = -40.261644278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -40.261644278 + -14 Combine like terms: 14 + -14 = 0 0 + x = -40.261644278 + -14 x = -40.261644278 + -14 Combine like terms: -40.261644278 + -14 = -54.261644278 x = -54.261644278 Simplifying x = -54.261644278Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.261644278, -54.261644278}Solution
x = {26.261644278, -54.261644278}
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