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Simplifying 15x2 + 36x = 31 Reorder the terms: 36x + 15x2 = 31 Solving 36x + 15x2 = 31 Solving for variable 'x'. Reorder the terms: -31 + 36x + 15x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 36x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.066666667 + 2.4x + x2 = 0 Move the constant term to the right: Add '2.066666667' to each side of the equation. -2.066666667 + 2.4x + 2.066666667 + x2 = 0 + 2.066666667 Reorder the terms: -2.066666667 + 2.066666667 + 2.4x + x2 = 0 + 2.066666667 Combine like terms: -2.066666667 + 2.066666667 = 0.000000000 0.000000000 + 2.4x + x2 = 0 + 2.066666667 2.4x + x2 = 0 + 2.066666667 Combine like terms: 0 + 2.066666667 = 2.066666667 2.4x + x2 = 2.066666667 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 2.066666667 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 2.066666667 + 1.44 Combine like terms: 2.066666667 + 1.44 = 3.506666667 1.44 + 2.4x + x2 = 3.506666667 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 3.506666667 Calculate the square root of the right side: 1.872609587 Break this problem into two subproblems by setting (x + 1.2) equal to 1.872609587 and -1.872609587.Subproblem 1
x + 1.2 = 1.872609587 Simplifying x + 1.2 = 1.872609587 Reorder the terms: 1.2 + x = 1.872609587 Solving 1.2 + x = 1.872609587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.872609587 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.872609587 + -1.2 x = 1.872609587 + -1.2 Combine like terms: 1.872609587 + -1.2 = 0.672609587 x = 0.672609587 Simplifying x = 0.672609587Subproblem 2
x + 1.2 = -1.872609587 Simplifying x + 1.2 = -1.872609587 Reorder the terms: 1.2 + x = -1.872609587 Solving 1.2 + x = -1.872609587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.872609587 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.872609587 + -1.2 x = -1.872609587 + -1.2 Combine like terms: -1.872609587 + -1.2 = -3.072609587 x = -3.072609587 Simplifying x = -3.072609587Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.672609587, -3.072609587}
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