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Simplifying 732 = 2x2 + 10x Reorder the terms: 732 = 10x + 2x2 Solving 732 = 10x + 2x2 Solving for variable 'x'. Reorder the terms: 732 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 732 + -10x + -2x2 = 0 + 2x2 + -2x2 732 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 732 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(366 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(366 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 366 + -5x + -1x2 = 0 Solving 366 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -366 + 5x + x2 = 0 Move the constant term to the right: Add '366' to each side of the equation. -366 + 5x + 366 + x2 = 0 + 366 Reorder the terms: -366 + 366 + 5x + x2 = 0 + 366 Combine like terms: -366 + 366 = 0 0 + 5x + x2 = 0 + 366 5x + x2 = 0 + 366 Combine like terms: 0 + 366 = 366 5x + x2 = 366 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 = 366 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 366 + 6.25 Combine like terms: 366 + 6.25 = 372.25 6.25 + 5x + x2 = 372.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 372.25 Calculate the square root of the right side: 19.293781382 Break this problem into two subproblems by setting (x + 2.5) equal to 19.293781382 and -19.293781382.Subproblem 1
x + 2.5 = 19.293781382 Simplifying x + 2.5 = 19.293781382 Reorder the terms: 2.5 + x = 19.293781382 Solving 2.5 + x = 19.293781382 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 = 19.293781382 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 19.293781382 + -2.5 x = 19.293781382 + -2.5 Combine like terms: 19.293781382 + -2.5 = 16.793781382 x = 16.793781382 Simplifying x = 16.793781382Subproblem 2
x + 2.5 = -19.293781382 Simplifying x + 2.5 = -19.293781382 Reorder the terms: 2.5 + x = -19.293781382 Solving 2.5 + x = -19.293781382 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 = -19.293781382 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -19.293781382 + -2.5 x = -19.293781382 + -2.5 Combine like terms: -19.293781382 + -2.5 = -21.793781382 x = -21.793781382 Simplifying x = -21.793781382Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.793781382, -21.793781382}Solution
x = {16.793781382, -21.793781382}
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