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Simplifying 153 = 20x(3x + -8) Reorder the terms: 153 = 20x(-8 + 3x) 153 = (-8 * 20x + 3x * 20x) 153 = (-160x + 60x2) Solving 153 = -160x + 60x2 Solving for variable 'x'. Reorder the terms: 153 + 160x + -60x2 = -160x + 160x + 60x2 + -60x2 Combine like terms: -160x + 160x = 0 153 + 160x + -60x2 = 0 + 60x2 + -60x2 153 + 160x + -60x2 = 60x2 + -60x2 Combine like terms: 60x2 + -60x2 = 0 153 + 160x + -60x2 = 0 Begin completing the square. Divide all terms by -60 the coefficient of the squared term: Divide each side by '-60'. -2.55 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '2.55' to each side of the equation. -2.55 + -2.666666667x + 2.55 + x2 = 0 + 2.55 Reorder the terms: -2.55 + 2.55 + -2.666666667x + x2 = 0 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + -2.666666667x + x2 = 0 + 2.55 -2.666666667x + x2 = 0 + 2.55 Combine like terms: 0 + 2.55 = 2.55 -2.666666667x + x2 = 2.55 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 = 2.55 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 2.55 + 1.777777780 Combine like terms: 2.55 + 1.777777780 = 4.32777778 1.777777780 + -2.666666667x + x2 = 4.32777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 4.32777778 Calculate the square root of the right side: 2.080331171 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.080331171 and -2.080331171.Subproblem 1
x + -1.333333334 = 2.080331171 Simplifying x + -1.333333334 = 2.080331171 Reorder the terms: -1.333333334 + x = 2.080331171 Solving -1.333333334 + x = 2.080331171 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 = 2.080331171 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.080331171 + 1.333333334 x = 2.080331171 + 1.333333334 Combine like terms: 2.080331171 + 1.333333334 = 3.413664505 x = 3.413664505 Simplifying x = 3.413664505Subproblem 2
x + -1.333333334 = -2.080331171 Simplifying x + -1.333333334 = -2.080331171 Reorder the terms: -1.333333334 + x = -2.080331171 Solving -1.333333334 + x = -2.080331171 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 = -2.080331171 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.080331171 + 1.333333334 x = -2.080331171 + 1.333333334 Combine like terms: -2.080331171 + 1.333333334 = -0.746997837 x = -0.746997837 Simplifying x = -0.746997837Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.413664505, -0.746997837}
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