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Simplifying x = -3x2 + 21x + 50 Reorder the terms: x = 50 + 21x + -3x2 Solving x = 50 + 21x + -3x2 Solving for variable 'x'. Reorder the terms: -50 + x + -21x + 3x2 = 50 + 21x + -3x2 + -50 + -21x + 3x2 Combine like terms: x + -21x = -20x -50 + -20x + 3x2 = 50 + 21x + -3x2 + -50 + -21x + 3x2 Reorder the terms: -50 + -20x + 3x2 = 50 + -50 + 21x + -21x + -3x2 + 3x2 Combine like terms: 50 + -50 = 0 -50 + -20x + 3x2 = 0 + 21x + -21x + -3x2 + 3x2 -50 + -20x + 3x2 = 21x + -21x + -3x2 + 3x2 Combine like terms: 21x + -21x = 0 -50 + -20x + 3x2 = 0 + -3x2 + 3x2 -50 + -20x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -50 + -20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + -6.666666667x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + -6.666666667x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + -6.666666667x + x2 = 0 + 16.66666667 -6.666666667x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 -6.666666667x + x2 = 16.66666667 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 = 16.66666667 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = 16.66666667 + 11.11111112 Combine like terms: 16.66666667 + 11.11111112 = 27.77777779 11.11111112 + -6.666666667x + x2 = 27.77777779 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 27.77777779 Calculate the square root of the right side: 5.270462768 Break this problem into two subproblems by setting (x + -3.333333334) equal to 5.270462768 and -5.270462768.Subproblem 1
x + -3.333333334 = 5.270462768 Simplifying x + -3.333333334 = 5.270462768 Reorder the terms: -3.333333334 + x = 5.270462768 Solving -3.333333334 + x = 5.270462768 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 = 5.270462768 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 5.270462768 + 3.333333334 x = 5.270462768 + 3.333333334 Combine like terms: 5.270462768 + 3.333333334 = 8.603796102 x = 8.603796102 Simplifying x = 8.603796102Subproblem 2
x + -3.333333334 = -5.270462768 Simplifying x + -3.333333334 = -5.270462768 Reorder the terms: -3.333333334 + x = -5.270462768 Solving -3.333333334 + x = -5.270462768 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 = -5.270462768 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -5.270462768 + 3.333333334 x = -5.270462768 + 3.333333334 Combine like terms: -5.270462768 + 3.333333334 = -1.937129434 x = -1.937129434 Simplifying x = -1.937129434Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.603796102, -1.937129434}
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