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Simplifying 180 = 2x(3x + 25) Reorder the terms: 180 = 2x(25 + 3x) 180 = (25 * 2x + 3x * 2x) 180 = (50x + 6x2) Solving 180 = 50x + 6x2 Solving for variable 'x'. Reorder the terms: 180 + -50x + -6x2 = 50x + -50x + 6x2 + -6x2 Combine like terms: 50x + -50x = 0 180 + -50x + -6x2 = 0 + 6x2 + -6x2 180 + -50x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 180 + -50x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -25x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -25x + -3x2)' equal to zero and attempt to solve: Simplifying 90 + -25x + -3x2 = 0 Solving 90 + -25x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -30 + 8.333333333x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 8.333333333x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 8.333333333x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 8.333333333x + x2 = 0 + 30 8.333333333x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 8.333333333x + x2 = 30 The x term is 8.333333333x. Take half its coefficient (4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. 8.333333333x + 17.36111111 + x2 = 30 + 17.36111111 Reorder the terms: 17.36111111 + 8.333333333x + x2 = 30 + 17.36111111 Combine like terms: 30 + 17.36111111 = 47.36111111 17.36111111 + 8.333333333x + x2 = 47.36111111 Factor a perfect square on the left side: (x + 4.166666667)(x + 4.166666667) = 47.36111111 Calculate the square root of the right side: 6.881940941 Break this problem into two subproblems by setting (x + 4.166666667) equal to 6.881940941 and -6.881940941.Subproblem 1
x + 4.166666667 = 6.881940941 Simplifying x + 4.166666667 = 6.881940941 Reorder the terms: 4.166666667 + x = 6.881940941 Solving 4.166666667 + x = 6.881940941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 6.881940941 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 6.881940941 + -4.166666667 x = 6.881940941 + -4.166666667 Combine like terms: 6.881940941 + -4.166666667 = 2.715274274 x = 2.715274274 Simplifying x = 2.715274274Subproblem 2
x + 4.166666667 = -6.881940941 Simplifying x + 4.166666667 = -6.881940941 Reorder the terms: 4.166666667 + x = -6.881940941 Solving 4.166666667 + x = -6.881940941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -6.881940941 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -6.881940941 + -4.166666667 x = -6.881940941 + -4.166666667 Combine like terms: -6.881940941 + -4.166666667 = -11.048607608 x = -11.048607608 Simplifying x = -11.048607608Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.715274274, -11.048607608}Solution
x = {2.715274274, -11.048607608}
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