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Simplifying 20x(3x + -28) = 537 Reorder the terms: 20x(-28 + 3x) = 537 (-28 * 20x + 3x * 20x) = 537 (-560x + 60x2) = 537 Solving -560x + 60x2 = 537 Solving for variable 'x'. Reorder the terms: -537 + -560x + 60x2 = 537 + -537 Combine like terms: 537 + -537 = 0 -537 + -560x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -8.95 + -9.333333333x + x2 = 0.0 Move the constant term to the right: Add '8.95' to each side of the equation. -8.95 + -9.333333333x + 8.95 + x2 = 0.0 + 8.95 Reorder the terms: -8.95 + 8.95 + -9.333333333x + x2 = 0.0 + 8.95 Combine like terms: -8.95 + 8.95 = 0.00 0.00 + -9.333333333x + x2 = 0.0 + 8.95 -9.333333333x + x2 = 0.0 + 8.95 Combine like terms: 0.0 + 8.95 = 8.95 -9.333333333x + x2 = 8.95 The x term is -9.333333333x. Take half its coefficient (-4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. -9.333333333x + 21.77777778 + x2 = 8.95 + 21.77777778 Reorder the terms: 21.77777778 + -9.333333333x + x2 = 8.95 + 21.77777778 Combine like terms: 8.95 + 21.77777778 = 30.72777778 21.77777778 + -9.333333333x + x2 = 30.72777778 Factor a perfect square on the left side: (x + -4.666666667)(x + -4.666666667) = 30.72777778 Calculate the square root of the right side: 5.543264181 Break this problem into two subproblems by setting (x + -4.666666667) equal to 5.543264181 and -5.543264181.Subproblem 1
x + -4.666666667 = 5.543264181 Simplifying x + -4.666666667 = 5.543264181 Reorder the terms: -4.666666667 + x = 5.543264181 Solving -4.666666667 + x = 5.543264181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = 5.543264181 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = 5.543264181 + 4.666666667 x = 5.543264181 + 4.666666667 Combine like terms: 5.543264181 + 4.666666667 = 10.209930848 x = 10.209930848 Simplifying x = 10.209930848Subproblem 2
x + -4.666666667 = -5.543264181 Simplifying x + -4.666666667 = -5.543264181 Reorder the terms: -4.666666667 + x = -5.543264181 Solving -4.666666667 + x = -5.543264181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = -5.543264181 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = -5.543264181 + 4.666666667 x = -5.543264181 + 4.666666667 Combine like terms: -5.543264181 + 4.666666667 = -0.876597514 x = -0.876597514 Simplifying x = -0.876597514Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.209930848, -0.876597514}
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