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Simplifying 460 = -360 + -105x + 5x2 Solving 460 = -360 + -105x + 5x2 Solving for variable 'x'. Combine like terms: 460 + 360 = 820 820 + 105x + -5x2 = -360 + -105x + 5x2 + 360 + 105x + -5x2 Reorder the terms: 820 + 105x + -5x2 = -360 + 360 + -105x + 105x + 5x2 + -5x2 Combine like terms: -360 + 360 = 0 820 + 105x + -5x2 = 0 + -105x + 105x + 5x2 + -5x2 820 + 105x + -5x2 = -105x + 105x + 5x2 + -5x2 Combine like terms: -105x + 105x = 0 820 + 105x + -5x2 = 0 + 5x2 + -5x2 820 + 105x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 820 + 105x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(164 + 21x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(164 + 21x + -1x2)' equal to zero and attempt to solve: Simplifying 164 + 21x + -1x2 = 0 Solving 164 + 21x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -164 + -21x + x2 = 0 Move the constant term to the right: Add '164' to each side of the equation. -164 + -21x + 164 + x2 = 0 + 164 Reorder the terms: -164 + 164 + -21x + x2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + -21x + x2 = 0 + 164 -21x + x2 = 0 + 164 Combine like terms: 0 + 164 = 164 -21x + x2 = 164 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 164 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 164 + 110.25 Combine like terms: 164 + 110.25 = 274.25 110.25 + -21x + x2 = 274.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 274.25 Calculate the square root of the right side: 16.560495162 Break this problem into two subproblems by setting (x + -10.5) equal to 16.560495162 and -16.560495162.Subproblem 1
x + -10.5 = 16.560495162 Simplifying x + -10.5 = 16.560495162 Reorder the terms: -10.5 + x = 16.560495162 Solving -10.5 + x = 16.560495162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 16.560495162 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 16.560495162 + 10.5 x = 16.560495162 + 10.5 Combine like terms: 16.560495162 + 10.5 = 27.060495162 x = 27.060495162 Simplifying x = 27.060495162Subproblem 2
x + -10.5 = -16.560495162 Simplifying x + -10.5 = -16.560495162 Reorder the terms: -10.5 + x = -16.560495162 Solving -10.5 + x = -16.560495162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -16.560495162 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -16.560495162 + 10.5 x = -16.560495162 + 10.5 Combine like terms: -16.560495162 + 10.5 = -6.060495162 x = -6.060495162 Simplifying x = -6.060495162Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.060495162, -6.060495162}Solution
x = {27.060495162, -6.060495162}
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