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Simplifying -2x2 + 4x + 52 = 0 Reorder the terms: 52 + 4x + -2x2 = 0 Solving 52 + 4x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(26 + 2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 26 + 2x + -1x2 = 0 Solving 26 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -26 + -2x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + -2x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -2x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -2x + x2 = 0 + 26 -2x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -2x + x2 = 26 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 = 26 + 1 Reorder the terms: 1 + -2x + x2 = 26 + 1 Combine like terms: 26 + 1 = 27 1 + -2x + x2 = 27 Factor a perfect square on the left side: (x + -1)(x + -1) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -1) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -1 = 5.196152423 Simplifying x + -1 = 5.196152423 Reorder the terms: -1 + x = 5.196152423 Solving -1 + x = 5.196152423 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 = 5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.196152423 + 1 x = 5.196152423 + 1 Combine like terms: 5.196152423 + 1 = 6.196152423 x = 6.196152423 Simplifying x = 6.196152423Subproblem 2
x + -1 = -5.196152423 Simplifying x + -1 = -5.196152423 Reorder the terms: -1 + x = -5.196152423 Solving -1 + x = -5.196152423 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 = -5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.196152423 + 1 x = -5.196152423 + 1 Combine like terms: -5.196152423 + 1 = -4.196152423 x = -4.196152423 Simplifying x = -4.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.196152423, -4.196152423}Solution
x = {6.196152423, -4.196152423}
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