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Simplifying 9x(3x + -20) = 74 Reorder the terms: 9x(-20 + 3x) = 74 (-20 * 9x + 3x * 9x) = 74 (-180x + 27x2) = 74 Solving -180x + 27x2 = 74 Solving for variable 'x'. Reorder the terms: -74 + -180x + 27x2 = 74 + -74 Combine like terms: 74 + -74 = 0 -74 + -180x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -2.740740741 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '2.740740741' to each side of the equation. -2.740740741 + -6.666666667x + 2.740740741 + x2 = 0 + 2.740740741 Reorder the terms: -2.740740741 + 2.740740741 + -6.666666667x + x2 = 0 + 2.740740741 Combine like terms: -2.740740741 + 2.740740741 = 0.000000000 0.000000000 + -6.666666667x + x2 = 0 + 2.740740741 -6.666666667x + x2 = 0 + 2.740740741 Combine like terms: 0 + 2.740740741 = 2.740740741 -6.666666667x + x2 = 2.740740741 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 = 2.740740741 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = 2.740740741 + 11.11111112 Combine like terms: 2.740740741 + 11.11111112 = 13.851851861 11.11111112 + -6.666666667x + x2 = 13.851851861 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 13.851851861 Calculate the square root of the right side: 3.721807607 Break this problem into two subproblems by setting (x + -3.333333334) equal to 3.721807607 and -3.721807607.Subproblem 1
x + -3.333333334 = 3.721807607 Simplifying x + -3.333333334 = 3.721807607 Reorder the terms: -3.333333334 + x = 3.721807607 Solving -3.333333334 + x = 3.721807607 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 = 3.721807607 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 3.721807607 + 3.333333334 x = 3.721807607 + 3.333333334 Combine like terms: 3.721807607 + 3.333333334 = 7.055140941 x = 7.055140941 Simplifying x = 7.055140941Subproblem 2
x + -3.333333334 = -3.721807607 Simplifying x + -3.333333334 = -3.721807607 Reorder the terms: -3.333333334 + x = -3.721807607 Solving -3.333333334 + x = -3.721807607 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 = -3.721807607 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -3.721807607 + 3.333333334 x = -3.721807607 + 3.333333334 Combine like terms: -3.721807607 + 3.333333334 = -0.388474273 x = -0.388474273 Simplifying x = -0.388474273Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.055140941, -0.388474273}
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