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Simplifying 15x2 + -36x = 103 Reorder the terms: -36x + 15x2 = 103 Solving -36x + 15x2 = 103 Solving for variable 'x'. Reorder the terms: -103 + -36x + 15x2 = 103 + -103 Combine like terms: 103 + -103 = 0 -103 + -36x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -6.866666667 + -2.4x + x2 = 0 Move the constant term to the right: Add '6.866666667' to each side of the equation. -6.866666667 + -2.4x + 6.866666667 + x2 = 0 + 6.866666667 Reorder the terms: -6.866666667 + 6.866666667 + -2.4x + x2 = 0 + 6.866666667 Combine like terms: -6.866666667 + 6.866666667 = 0.000000000 0.000000000 + -2.4x + x2 = 0 + 6.866666667 -2.4x + x2 = 0 + 6.866666667 Combine like terms: 0 + 6.866666667 = 6.866666667 -2.4x + x2 = 6.866666667 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 = 6.866666667 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 6.866666667 + 1.44 Combine like terms: 6.866666667 + 1.44 = 8.306666667 1.44 + -2.4x + x2 = 8.306666667 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 8.306666667 Calculate the square root of the right side: 2.882128843 Break this problem into two subproblems by setting (x + -1.2) equal to 2.882128843 and -2.882128843.Subproblem 1
x + -1.2 = 2.882128843 Simplifying x + -1.2 = 2.882128843 Reorder the terms: -1.2 + x = 2.882128843 Solving -1.2 + x = 2.882128843 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 = 2.882128843 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.882128843 + 1.2 x = 2.882128843 + 1.2 Combine like terms: 2.882128843 + 1.2 = 4.082128843 x = 4.082128843 Simplifying x = 4.082128843Subproblem 2
x + -1.2 = -2.882128843 Simplifying x + -1.2 = -2.882128843 Reorder the terms: -1.2 + x = -2.882128843 Solving -1.2 + x = -2.882128843 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 = -2.882128843 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.882128843 + 1.2 x = -2.882128843 + 1.2 Combine like terms: -2.882128843 + 1.2 = -1.682128843 x = -1.682128843 Simplifying x = -1.682128843Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.082128843, -1.682128843}
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