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Simplifying 15x2 + 70x + -81 = 0 Reorder the terms: -81 + 70x + 15x2 = 0 Solving -81 + 70x + 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'. -5.4 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 4.666666667x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 4.666666667x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 4.666666667x + x2 = 0 + 5.4 4.666666667x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 4.666666667x + x2 = 5.4 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 5.4 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 5.4 + 5.444444448 Combine like terms: 5.4 + 5.444444448 = 10.844444448 5.444444448 + 4.666666667x + x2 = 10.844444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 10.844444448 Calculate the square root of the right side: 3.29309041 Break this problem into two subproblems by setting (x + 2.333333334) equal to 3.29309041 and -3.29309041.Subproblem 1
x + 2.333333334 = 3.29309041 Simplifying x + 2.333333334 = 3.29309041 Reorder the terms: 2.333333334 + x = 3.29309041 Solving 2.333333334 + x = 3.29309041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 3.29309041 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 3.29309041 + -2.333333334 x = 3.29309041 + -2.333333334 Combine like terms: 3.29309041 + -2.333333334 = 0.959757076 x = 0.959757076 Simplifying x = 0.959757076Subproblem 2
x + 2.333333334 = -3.29309041 Simplifying x + 2.333333334 = -3.29309041 Reorder the terms: 2.333333334 + x = -3.29309041 Solving 2.333333334 + x = -3.29309041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -3.29309041 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -3.29309041 + -2.333333334 x = -3.29309041 + -2.333333334 Combine like terms: -3.29309041 + -2.333333334 = -5.626423744 x = -5.626423744 Simplifying x = -5.626423744Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.959757076, -5.626423744}
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