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Simplifying 5x + 3x(2x + 5) = 180 Reorder the terms: 5x + 3x(5 + 2x) = 180 5x + (5 * 3x + 2x * 3x) = 180 5x + (15x + 6x2) = 180 Combine like terms: 5x + 15x = 20x 20x + 6x2 = 180 Solving 20x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 20x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 20x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 10x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 10x + 3x2)' equal to zero and attempt to solve: Simplifying -90 + 10x + 3x2 = 0 Solving -90 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 3.333333333x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 3.333333333x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 3.333333333x + x2 = 0 + 30 3.333333333x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 3.333333333x + x2 = 30 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 30 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 30 + 2.777777779 Combine like terms: 30 + 2.777777779 = 32.777777779 2.777777779 + 3.333333333x + x2 = 32.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 32.777777779 Calculate the square root of the right side: 5.725188013 Break this problem into two subproblems by setting (x + 1.666666667) equal to 5.725188013 and -5.725188013.Subproblem 1
x + 1.666666667 = 5.725188013 Simplifying x + 1.666666667 = 5.725188013 Reorder the terms: 1.666666667 + x = 5.725188013 Solving 1.666666667 + x = 5.725188013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 5.725188013 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 5.725188013 + -1.666666667 x = 5.725188013 + -1.666666667 Combine like terms: 5.725188013 + -1.666666667 = 4.058521346 x = 4.058521346 Simplifying x = 4.058521346Subproblem 2
x + 1.666666667 = -5.725188013 Simplifying x + 1.666666667 = -5.725188013 Reorder the terms: 1.666666667 + x = -5.725188013 Solving 1.666666667 + x = -5.725188013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -5.725188013 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -5.725188013 + -1.666666667 x = -5.725188013 + -1.666666667 Combine like terms: -5.725188013 + -1.666666667 = -7.39185468 x = -7.39185468 Simplifying x = -7.39185468Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.058521346, -7.39185468}Solution
x = {4.058521346, -7.39185468}
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