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Simplifying 0 = 2x2 + 10x + -936 Reorder the terms: 0 = -936 + 10x + 2x2 Solving 0 = -936 + 10x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 936 = 936 936 + -10x + -2x2 = -936 + 10x + 2x2 + 936 + -10x + -2x2 Reorder the terms: 936 + -10x + -2x2 = -936 + 936 + 10x + -10x + 2x2 + -2x2 Combine like terms: -936 + 936 = 0 936 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2 936 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 936 + -10x + -2x2 = 0 + 2x2 + -2x2 936 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 936 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(468 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(468 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 468 + -5x + -1x2 = 0 Solving 468 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -468 + 5x + x2 = 0 Move the constant term to the right: Add '468' to each side of the equation. -468 + 5x + 468 + x2 = 0 + 468 Reorder the terms: -468 + 468 + 5x + x2 = 0 + 468 Combine like terms: -468 + 468 = 0 0 + 5x + x2 = 0 + 468 5x + x2 = 0 + 468 Combine like terms: 0 + 468 = 468 5x + x2 = 468 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 468 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 468 + 6.25 Combine like terms: 468 + 6.25 = 474.25 6.25 + 5x + x2 = 474.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 474.25 Calculate the square root of the right side: 21.77728174 Break this problem into two subproblems by setting (x + 2.5) equal to 21.77728174 and -21.77728174.Subproblem 1
x + 2.5 = 21.77728174 Simplifying x + 2.5 = 21.77728174 Reorder the terms: 2.5 + x = 21.77728174 Solving 2.5 + x = 21.77728174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 21.77728174 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 21.77728174 + -2.5 x = 21.77728174 + -2.5 Combine like terms: 21.77728174 + -2.5 = 19.27728174 x = 19.27728174 Simplifying x = 19.27728174Subproblem 2
x + 2.5 = -21.77728174 Simplifying x + 2.5 = -21.77728174 Reorder the terms: 2.5 + x = -21.77728174 Solving 2.5 + x = -21.77728174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -21.77728174 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -21.77728174 + -2.5 x = -21.77728174 + -2.5 Combine like terms: -21.77728174 + -2.5 = -24.27728174 x = -24.27728174 Simplifying x = -24.27728174Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.27728174, -24.27728174}Solution
x = {19.27728174, -24.27728174}
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