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Simplifying 15x2 + 40x + 16 = 0 Reorder the terms: 16 + 40x + 15x2 = 0 Solving 16 + 40x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.066666667 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-1.066666667' to each side of the equation. 1.066666667 + 2.666666667x + -1.066666667 + x2 = 0 + -1.066666667 Reorder the terms: 1.066666667 + -1.066666667 + 2.666666667x + x2 = 0 + -1.066666667 Combine like terms: 1.066666667 + -1.066666667 = 0.000000000 0.000000000 + 2.666666667x + x2 = 0 + -1.066666667 2.666666667x + x2 = 0 + -1.066666667 Combine like terms: 0 + -1.066666667 = -1.066666667 2.666666667x + x2 = -1.066666667 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 = -1.066666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -1.066666667 + 1.777777780 Combine like terms: -1.066666667 + 1.777777780 = 0.711111113 1.777777780 + 2.666666667x + x2 = 0.711111113 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 0.711111113 Calculate the square root of the right side: 0.843274044 Break this problem into two subproblems by setting (x + 1.333333334) equal to 0.843274044 and -0.843274044.Subproblem 1
x + 1.333333334 = 0.843274044 Simplifying x + 1.333333334 = 0.843274044 Reorder the terms: 1.333333334 + x = 0.843274044 Solving 1.333333334 + x = 0.843274044 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 = 0.843274044 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 0.843274044 + -1.333333334 x = 0.843274044 + -1.333333334 Combine like terms: 0.843274044 + -1.333333334 = -0.49005929 x = -0.49005929 Simplifying x = -0.49005929Subproblem 2
x + 1.333333334 = -0.843274044 Simplifying x + 1.333333334 = -0.843274044 Reorder the terms: 1.333333334 + x = -0.843274044 Solving 1.333333334 + x = -0.843274044 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 = -0.843274044 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -0.843274044 + -1.333333334 x = -0.843274044 + -1.333333334 Combine like terms: -0.843274044 + -1.333333334 = -2.176607378 x = -2.176607378 Simplifying x = -2.176607378Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.49005929, -2.176607378}
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