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Simplifying 3x2 + 8x + -75 = 0 Reorder the terms: -75 + 8x + 3x2 = 0 Solving -75 + 8x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 2.666666667x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 2.666666667x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2.666666667x + x2 = 0 + 25 2.666666667x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 2.666666667x + x2 = 25 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 = 25 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 25 + 1.777777780 Combine like terms: 25 + 1.777777780 = 26.77777778 1.777777780 + 2.666666667x + x2 = 26.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 26.77777778 Calculate the square root of the right side: 5.174724899 Break this problem into two subproblems by setting (x + 1.333333334) equal to 5.174724899 and -5.174724899.Subproblem 1
x + 1.333333334 = 5.174724899 Simplifying x + 1.333333334 = 5.174724899 Reorder the terms: 1.333333334 + x = 5.174724899 Solving 1.333333334 + x = 5.174724899 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 = 5.174724899 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 5.174724899 + -1.333333334 x = 5.174724899 + -1.333333334 Combine like terms: 5.174724899 + -1.333333334 = 3.841391565 x = 3.841391565 Simplifying x = 3.841391565Subproblem 2
x + 1.333333334 = -5.174724899 Simplifying x + 1.333333334 = -5.174724899 Reorder the terms: 1.333333334 + x = -5.174724899 Solving 1.333333334 + x = -5.174724899 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 = -5.174724899 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -5.174724899 + -1.333333334 x = -5.174724899 + -1.333333334 Combine like terms: -5.174724899 + -1.333333334 = -6.508058233 x = -6.508058233 Simplifying x = -6.508058233Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.841391565, -6.508058233}
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