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Simplifying 4x2 + 104x + -450 = 0 Reorder the terms: -450 + 104x + 4x2 = 0 Solving -450 + 104x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-225 + 52x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-225 + 52x + 2x2)' equal to zero and attempt to solve: Simplifying -225 + 52x + 2x2 = 0 Solving -225 + 52x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -112.5 + 26x + x2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + 26x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + 26x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + 26x + x2 = 0 + 112.5 26x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 26x + x2 = 112.5 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 112.5 + 169 Reorder the terms: 169 + 26x + x2 = 112.5 + 169 Combine like terms: 112.5 + 169 = 281.5 169 + 26x + x2 = 281.5 Factor a perfect square on the left side: (x + 13)(x + 13) = 281.5 Calculate the square root of the right side: 16.777961736 Break this problem into two subproblems by setting (x + 13) equal to 16.777961736 and -16.777961736.Subproblem 1
x + 13 = 16.777961736 Simplifying x + 13 = 16.777961736 Reorder the terms: 13 + x = 16.777961736 Solving 13 + x = 16.777961736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 16.777961736 + -13 Combine like terms: 13 + -13 = 0 0 + x = 16.777961736 + -13 x = 16.777961736 + -13 Combine like terms: 16.777961736 + -13 = 3.777961736 x = 3.777961736 Simplifying x = 3.777961736Subproblem 2
x + 13 = -16.777961736 Simplifying x + 13 = -16.777961736 Reorder the terms: 13 + x = -16.777961736 Solving 13 + x = -16.777961736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -16.777961736 + -13 Combine like terms: 13 + -13 = 0 0 + x = -16.777961736 + -13 x = -16.777961736 + -13 Combine like terms: -16.777961736 + -13 = -29.777961736 x = -29.777961736 Simplifying x = -29.777961736Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.777961736, -29.777961736}Solution
x = {3.777961736, -29.777961736}
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