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Simplifying 2x2 + -4x + 4 = 628 Reorder the terms: 4 + -4x + 2x2 = 628 Solving 4 + -4x + 2x2 = 628 Solving for variable 'x'. Reorder the terms: 4 + -628 + -4x + 2x2 = 628 + -628 Combine like terms: 4 + -628 = -624 -624 + -4x + 2x2 = 628 + -628 Combine like terms: 628 + -628 = 0 -624 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-312 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-312 + -2x + x2)' equal to zero and attempt to solve: Simplifying -312 + -2x + x2 = 0 Solving -312 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '312' to each side of the equation. -312 + -2x + 312 + x2 = 0 + 312 Reorder the terms: -312 + 312 + -2x + x2 = 0 + 312 Combine like terms: -312 + 312 = 0 0 + -2x + x2 = 0 + 312 -2x + x2 = 0 + 312 Combine like terms: 0 + 312 = 312 -2x + x2 = 312 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 = 312 + 1 Reorder the terms: 1 + -2x + x2 = 312 + 1 Combine like terms: 312 + 1 = 313 1 + -2x + x2 = 313 Factor a perfect square on the left side: (x + -1)(x + -1) = 313 Calculate the square root of the right side: 17.691806013 Break this problem into two subproblems by setting (x + -1) equal to 17.691806013 and -17.691806013.Subproblem 1
x + -1 = 17.691806013 Simplifying x + -1 = 17.691806013 Reorder the terms: -1 + x = 17.691806013 Solving -1 + x = 17.691806013 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 = 17.691806013 + 1 Combine like terms: -1 + 1 = 0 0 + x = 17.691806013 + 1 x = 17.691806013 + 1 Combine like terms: 17.691806013 + 1 = 18.691806013 x = 18.691806013 Simplifying x = 18.691806013Subproblem 2
x + -1 = -17.691806013 Simplifying x + -1 = -17.691806013 Reorder the terms: -1 + x = -17.691806013 Solving -1 + x = -17.691806013 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 = -17.691806013 + 1 Combine like terms: -1 + 1 = 0 0 + x = -17.691806013 + 1 x = -17.691806013 + 1 Combine like terms: -17.691806013 + 1 = -16.691806013 x = -16.691806013 Simplifying x = -16.691806013Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.691806013, -16.691806013}Solution
x = {18.691806013, -16.691806013}
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