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Simplifying 2x2 + 4x + 4 = 1258 Reorder the terms: 4 + 4x + 2x2 = 1258 Solving 4 + 4x + 2x2 = 1258 Solving for variable 'x'. Reorder the terms: 4 + -1258 + 4x + 2x2 = 1258 + -1258 Combine like terms: 4 + -1258 = -1254 -1254 + 4x + 2x2 = 1258 + -1258 Combine like terms: 1258 + -1258 = 0 -1254 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-627 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-627 + 2x + x2)' equal to zero and attempt to solve: Simplifying -627 + 2x + x2 = 0 Solving -627 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '627' to each side of the equation. -627 + 2x + 627 + x2 = 0 + 627 Reorder the terms: -627 + 627 + 2x + x2 = 0 + 627 Combine like terms: -627 + 627 = 0 0 + 2x + x2 = 0 + 627 2x + x2 = 0 + 627 Combine like terms: 0 + 627 = 627 2x + x2 = 627 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 = 627 + 1 Reorder the terms: 1 + 2x + x2 = 627 + 1 Combine like terms: 627 + 1 = 628 1 + 2x + x2 = 628 Factor a perfect square on the left side: (x + 1)(x + 1) = 628 Calculate the square root of the right side: 25.059928172 Break this problem into two subproblems by setting (x + 1) equal to 25.059928172 and -25.059928172.Subproblem 1
x + 1 = 25.059928172 Simplifying x + 1 = 25.059928172 Reorder the terms: 1 + x = 25.059928172 Solving 1 + x = 25.059928172 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 = 25.059928172 + -1 Combine like terms: 1 + -1 = 0 0 + x = 25.059928172 + -1 x = 25.059928172 + -1 Combine like terms: 25.059928172 + -1 = 24.059928172 x = 24.059928172 Simplifying x = 24.059928172Subproblem 2
x + 1 = -25.059928172 Simplifying x + 1 = -25.059928172 Reorder the terms: 1 + x = -25.059928172 Solving 1 + x = -25.059928172 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 = -25.059928172 + -1 Combine like terms: 1 + -1 = 0 0 + x = -25.059928172 + -1 x = -25.059928172 + -1 Combine like terms: -25.059928172 + -1 = -26.059928172 x = -26.059928172 Simplifying x = -26.059928172Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.059928172, -26.059928172}Solution
x = {24.059928172, -26.059928172}
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