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Simplifying 2x2 + -14x = 392 Reorder the terms: -14x + 2x2 = 392 Solving -14x + 2x2 = 392 Solving for variable 'x'. Reorder the terms: -392 + -14x + 2x2 = 392 + -392 Combine like terms: 392 + -392 = 0 -392 + -14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-196 + -7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-196 + -7x + x2)' equal to zero and attempt to solve: Simplifying -196 + -7x + x2 = 0 Solving -196 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + -7x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + -7x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + -7x + x2 = 0 + 196 -7x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 -7x + x2 = 196 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 196 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 196 + 12.25 Combine like terms: 196 + 12.25 = 208.25 12.25 + -7x + x2 = 208.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 208.25 Calculate the square root of the right side: 14.43086969 Break this problem into two subproblems by setting (x + -3.5) equal to 14.43086969 and -14.43086969.Subproblem 1
x + -3.5 = 14.43086969 Simplifying x + -3.5 = 14.43086969 Reorder the terms: -3.5 + x = 14.43086969 Solving -3.5 + x = 14.43086969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 14.43086969 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 14.43086969 + 3.5 x = 14.43086969 + 3.5 Combine like terms: 14.43086969 + 3.5 = 17.93086969 x = 17.93086969 Simplifying x = 17.93086969Subproblem 2
x + -3.5 = -14.43086969 Simplifying x + -3.5 = -14.43086969 Reorder the terms: -3.5 + x = -14.43086969 Solving -3.5 + x = -14.43086969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -14.43086969 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -14.43086969 + 3.5 x = -14.43086969 + 3.5 Combine like terms: -14.43086969 + 3.5 = -10.93086969 x = -10.93086969 Simplifying x = -10.93086969Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.93086969, -10.93086969}Solution
x = {17.93086969, -10.93086969}
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