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Simplifying 3x2 + -8x = 45 Reorder the terms: -8x + 3x2 = 45 Solving -8x + 3x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -8x + 3x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -2.666666667x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -2.666666667x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2.666666667x + x2 = 0 + 15 -2.666666667x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -2.666666667x + x2 = 15 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 = 15 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 15 + 1.777777780 Combine like terms: 15 + 1.777777780 = 16.77777778 1.777777780 + -2.666666667x + x2 = 16.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 16.77777778 Calculate the square root of the right side: 4.096068576 Break this problem into two subproblems by setting (x + -1.333333334) equal to 4.096068576 and -4.096068576.Subproblem 1
x + -1.333333334 = 4.096068576 Simplifying x + -1.333333334 = 4.096068576 Reorder the terms: -1.333333334 + x = 4.096068576 Solving -1.333333334 + x = 4.096068576 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 = 4.096068576 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 4.096068576 + 1.333333334 x = 4.096068576 + 1.333333334 Combine like terms: 4.096068576 + 1.333333334 = 5.42940191 x = 5.42940191 Simplifying x = 5.42940191Subproblem 2
x + -1.333333334 = -4.096068576 Simplifying x + -1.333333334 = -4.096068576 Reorder the terms: -1.333333334 + x = -4.096068576 Solving -1.333333334 + x = -4.096068576 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 = -4.096068576 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -4.096068576 + 1.333333334 x = -4.096068576 + 1.333333334 Combine like terms: -4.096068576 + 1.333333334 = -2.762735242 x = -2.762735242 Simplifying x = -2.762735242Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.42940191, -2.762735242}
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