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Simplifying 3x2 + -8x + 18 = 523 Reorder the terms: 18 + -8x + 3x2 = 523 Solving 18 + -8x + 3x2 = 523 Solving for variable 'x'. Reorder the terms: 18 + -523 + -8x + 3x2 = 523 + -523 Combine like terms: 18 + -523 = -505 -505 + -8x + 3x2 = 523 + -523 Combine like terms: 523 + -523 = 0 -505 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -168.3333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '168.3333333' to each side of the equation. -168.3333333 + -2.666666667x + 168.3333333 + x2 = 0 + 168.3333333 Reorder the terms: -168.3333333 + 168.3333333 + -2.666666667x + x2 = 0 + 168.3333333 Combine like terms: -168.3333333 + 168.3333333 = 0.0000000 0.0000000 + -2.666666667x + x2 = 0 + 168.3333333 -2.666666667x + x2 = 0 + 168.3333333 Combine like terms: 0 + 168.3333333 = 168.3333333 -2.666666667x + x2 = 168.3333333 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 168.3333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 168.3333333 + 1.777777780 Combine like terms: 168.3333333 + 1.777777780 = 170.11111108 1.777777780 + -2.666666667x + x2 = 170.11111108 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 170.11111108 Calculate the square root of the right side: 13.04266503 Break this problem into two subproblems by setting (x + -1.333333334) equal to 13.04266503 and -13.04266503.Subproblem 1
x + -1.333333334 = 13.04266503 Simplifying x + -1.333333334 = 13.04266503 Reorder the terms: -1.333333334 + x = 13.04266503 Solving -1.333333334 + x = 13.04266503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 13.04266503 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 13.04266503 + 1.333333334 x = 13.04266503 + 1.333333334 Combine like terms: 13.04266503 + 1.333333334 = 14.375998364 x = 14.375998364 Simplifying x = 14.375998364Subproblem 2
x + -1.333333334 = -13.04266503 Simplifying x + -1.333333334 = -13.04266503 Reorder the terms: -1.333333334 + x = -13.04266503 Solving -1.333333334 + x = -13.04266503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -13.04266503 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -13.04266503 + 1.333333334 x = -13.04266503 + 1.333333334 Combine like terms: -13.04266503 + 1.333333334 = -11.709331696 x = -11.709331696 Simplifying x = -11.709331696Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.375998364, -11.709331696}
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