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Simplifying 84 = 3x2 + 8x Reorder the terms: 84 = 8x + 3x2 Solving 84 = 8x + 3x2 Solving for variable 'x'. Reorder the terms: 84 + -8x + -3x2 = 8x + -8x + 3x2 + -3x2 Combine like terms: 8x + -8x = 0 84 + -8x + -3x2 = 0 + 3x2 + -3x2 84 + -8x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 84 + -8x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -28 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 2.666666667x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 2.666666667x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 2.666666667x + x2 = 0 + 28 2.666666667x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 2.666666667x + x2 = 28 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 = 28 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 28 + 1.777777780 Combine like terms: 28 + 1.777777780 = 29.77777778 1.777777780 + 2.666666667x + x2 = 29.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 29.77777778 Calculate the square root of the right side: 5.456901848 Break this problem into two subproblems by setting (x + 1.333333334) equal to 5.456901848 and -5.456901848.Subproblem 1
x + 1.333333334 = 5.456901848 Simplifying x + 1.333333334 = 5.456901848 Reorder the terms: 1.333333334 + x = 5.456901848 Solving 1.333333334 + x = 5.456901848 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 = 5.456901848 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 5.456901848 + -1.333333334 x = 5.456901848 + -1.333333334 Combine like terms: 5.456901848 + -1.333333334 = 4.123568514 x = 4.123568514 Simplifying x = 4.123568514Subproblem 2
x + 1.333333334 = -5.456901848 Simplifying x + 1.333333334 = -5.456901848 Reorder the terms: 1.333333334 + x = -5.456901848 Solving 1.333333334 + x = -5.456901848 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 = -5.456901848 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -5.456901848 + -1.333333334 x = -5.456901848 + -1.333333334 Combine like terms: -5.456901848 + -1.333333334 = -6.790235182 x = -6.790235182 Simplifying x = -6.790235182Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.123568514, -6.790235182}
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