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Simplifying 15x2 + 61x + -20 = 0 Reorder the terms: -20 + 61x + 15x2 = 0 Solving -20 + 61x + 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'. -1.333333333 + 4.066666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 4.066666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 4.066666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 4.066666667x + x2 = 0 + 1.333333333 4.066666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 4.066666667x + x2 = 1.333333333 The x term is 4.066666667x. Take half its coefficient (2.033333334). Square it (4.134444447) and add it to both sides. Add '4.134444447' to each side of the equation. 4.066666667x + 4.134444447 + x2 = 1.333333333 + 4.134444447 Reorder the terms: 4.134444447 + 4.066666667x + x2 = 1.333333333 + 4.134444447 Combine like terms: 1.333333333 + 4.134444447 = 5.46777778 4.134444447 + 4.066666667x + x2 = 5.46777778 Factor a perfect square on the left side: (x + 2.033333334)(x + 2.033333334) = 5.46777778 Calculate the square root of the right side: 2.338327988 Break this problem into two subproblems by setting (x + 2.033333334) equal to 2.338327988 and -2.338327988.Subproblem 1
x + 2.033333334 = 2.338327988 Simplifying x + 2.033333334 = 2.338327988 Reorder the terms: 2.033333334 + x = 2.338327988 Solving 2.033333334 + x = 2.338327988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.033333334' to each side of the equation. 2.033333334 + -2.033333334 + x = 2.338327988 + -2.033333334 Combine like terms: 2.033333334 + -2.033333334 = 0.000000000 0.000000000 + x = 2.338327988 + -2.033333334 x = 2.338327988 + -2.033333334 Combine like terms: 2.338327988 + -2.033333334 = 0.304994654 x = 0.304994654 Simplifying x = 0.304994654Subproblem 2
x + 2.033333334 = -2.338327988 Simplifying x + 2.033333334 = -2.338327988 Reorder the terms: 2.033333334 + x = -2.338327988 Solving 2.033333334 + x = -2.338327988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.033333334' to each side of the equation. 2.033333334 + -2.033333334 + x = -2.338327988 + -2.033333334 Combine like terms: 2.033333334 + -2.033333334 = 0.000000000 0.000000000 + x = -2.338327988 + -2.033333334 x = -2.338327988 + -2.033333334 Combine like terms: -2.338327988 + -2.033333334 = -4.371661322 x = -4.371661322 Simplifying x = -4.371661322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.304994654, -4.371661322}
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