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Simplifying (5x)(3x + -1) = 180 Remove parenthesis around (5x) 5x(3x + -1) = 180 Reorder the terms: 5x(-1 + 3x) = 180 (-1 * 5x + 3x * 5x) = 180 (-5x + 15x2) = 180 Solving -5x + 15x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -5x + 15x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -5x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + -1x + 3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -36 + -1x + 3x2 = 0 Solving -36 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.3333333333x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -0.3333333333x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.3333333333x + x2 = 0 + 12 -0.3333333333x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.3333333333x + x2 = 12 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 12 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 12 + 0.02777777779 Combine like terms: 12 + 0.02777777779 = 12.02777777779 0.02777777779 + -0.3333333333x + x2 = 12.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 12.02777777779 Calculate the square root of the right side: 3.468108674 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 3.468108674 and -3.468108674.Subproblem 1
x + -0.1666666667 = 3.468108674 Simplifying x + -0.1666666667 = 3.468108674 Reorder the terms: -0.1666666667 + x = 3.468108674 Solving -0.1666666667 + x = 3.468108674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 3.468108674 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 3.468108674 + 0.1666666667 x = 3.468108674 + 0.1666666667 Combine like terms: 3.468108674 + 0.1666666667 = 3.6347753407 x = 3.6347753407 Simplifying x = 3.6347753407Subproblem 2
x + -0.1666666667 = -3.468108674 Simplifying x + -0.1666666667 = -3.468108674 Reorder the terms: -0.1666666667 + x = -3.468108674 Solving -0.1666666667 + x = -3.468108674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -3.468108674 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -3.468108674 + 0.1666666667 x = -3.468108674 + 0.1666666667 Combine like terms: -3.468108674 + 0.1666666667 = -3.3014420073 x = -3.3014420073 Simplifying x = -3.3014420073Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6347753407, -3.3014420073}Solution
x = {3.6347753407, -3.3014420073}
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