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Simplifying 2x(3x + -5) = 196 Reorder the terms: 2x(-5 + 3x) = 196 (-5 * 2x + 3x * 2x) = 196 (-10x + 6x2) = 196 Solving -10x + 6x2 = 196 Solving for variable 'x'. Reorder the terms: -196 + -10x + 6x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -196 + -10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-98 + -5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-98 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -98 + -5x + 3x2 = 0 Solving -98 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -32.66666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '32.66666667' to each side of the equation. -32.66666667 + -1.666666667x + 32.66666667 + x2 = 0 + 32.66666667 Reorder the terms: -32.66666667 + 32.66666667 + -1.666666667x + x2 = 0 + 32.66666667 Combine like terms: -32.66666667 + 32.66666667 = 0.00000000 0.00000000 + -1.666666667x + x2 = 0 + 32.66666667 -1.666666667x + x2 = 0 + 32.66666667 Combine like terms: 0 + 32.66666667 = 32.66666667 -1.666666667x + x2 = 32.66666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 32.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 32.66666667 + 0.6944444447 Combine like terms: 32.66666667 + 0.6944444447 = 33.3611111147 0.6944444447 + -1.666666667x + x2 = 33.3611111147 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 33.3611111147 Calculate the square root of the right side: 5.775907817 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 5.775907817 and -5.775907817.Subproblem 1
x + -0.8333333335 = 5.775907817 Simplifying x + -0.8333333335 = 5.775907817 Reorder the terms: -0.8333333335 + x = 5.775907817 Solving -0.8333333335 + x = 5.775907817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 5.775907817 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 5.775907817 + 0.8333333335 x = 5.775907817 + 0.8333333335 Combine like terms: 5.775907817 + 0.8333333335 = 6.6092411505 x = 6.6092411505 Simplifying x = 6.6092411505Subproblem 2
x + -0.8333333335 = -5.775907817 Simplifying x + -0.8333333335 = -5.775907817 Reorder the terms: -0.8333333335 + x = -5.775907817 Solving -0.8333333335 + x = -5.775907817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -5.775907817 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -5.775907817 + 0.8333333335 x = -5.775907817 + 0.8333333335 Combine like terms: -5.775907817 + 0.8333333335 = -4.9425744835 x = -4.9425744835 Simplifying x = -4.9425744835Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6092411505, -4.9425744835}Solution
x = {6.6092411505, -4.9425744835}
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