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Simplifying 180 = 2x(3x + 20) Reorder the terms: 180 = 2x(20 + 3x) 180 = (20 * 2x + 3x * 2x) 180 = (40x + 6x2) Solving 180 = 40x + 6x2 Solving for variable 'x'. Reorder the terms: 180 + -40x + -6x2 = 40x + -40x + 6x2 + -6x2 Combine like terms: 40x + -40x = 0 180 + -40x + -6x2 = 0 + 6x2 + -6x2 180 + -40x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 180 + -40x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -20x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -20x + -3x2)' equal to zero and attempt to solve: Simplifying 90 + -20x + -3x2 = 0 Solving 90 + -20x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -30 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 6.666666667x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 6.666666667x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 6.666666667x + x2 = 0 + 30 6.666666667x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 6.666666667x + x2 = 30 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 30 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 30 + 11.11111112 Combine like terms: 30 + 11.11111112 = 41.11111112 11.11111112 + 6.666666667x + x2 = 41.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 41.11111112 Calculate the square root of the right side: 6.411794688 Break this problem into two subproblems by setting (x + 3.333333334) equal to 6.411794688 and -6.411794688.Subproblem 1
x + 3.333333334 = 6.411794688 Simplifying x + 3.333333334 = 6.411794688 Reorder the terms: 3.333333334 + x = 6.411794688 Solving 3.333333334 + x = 6.411794688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 6.411794688 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 6.411794688 + -3.333333334 x = 6.411794688 + -3.333333334 Combine like terms: 6.411794688 + -3.333333334 = 3.078461354 x = 3.078461354 Simplifying x = 3.078461354Subproblem 2
x + 3.333333334 = -6.411794688 Simplifying x + 3.333333334 = -6.411794688 Reorder the terms: 3.333333334 + x = -6.411794688 Solving 3.333333334 + x = -6.411794688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -6.411794688 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -6.411794688 + -3.333333334 x = -6.411794688 + -3.333333334 Combine like terms: -6.411794688 + -3.333333334 = -9.745128022 x = -9.745128022 Simplifying x = -9.745128022Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.078461354, -9.745128022}Solution
x = {3.078461354, -9.745128022}
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