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Simplifying 15 = 6x2 + -23x + -15 Reorder the terms: 15 = -15 + -23x + 6x2 Solving 15 = -15 + -23x + 6x2 Solving for variable 'x'. Combine like terms: 15 + 15 = 30 30 + 23x + -6x2 = -15 + -23x + 6x2 + 15 + 23x + -6x2 Reorder the terms: 30 + 23x + -6x2 = -15 + 15 + -23x + 23x + 6x2 + -6x2 Combine like terms: -15 + 15 = 0 30 + 23x + -6x2 = 0 + -23x + 23x + 6x2 + -6x2 30 + 23x + -6x2 = -23x + 23x + 6x2 + -6x2 Combine like terms: -23x + 23x = 0 30 + 23x + -6x2 = 0 + 6x2 + -6x2 30 + 23x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 30 + 23x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -5 + -3.833333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -3.833333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -3.833333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3.833333333x + x2 = 0 + 5 -3.833333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3.833333333x + x2 = 5 The x term is -3.833333333x. Take half its coefficient (-1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. -3.833333333x + 3.673611112 + x2 = 5 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333x + x2 = 5 + 3.673611112 Combine like terms: 5 + 3.673611112 = 8.673611112 3.673611112 + -3.833333333x + x2 = 8.673611112 Factor a perfect square on the left side: (x + -1.916666667)(x + -1.916666667) = 8.673611112 Calculate the square root of the right side: 2.945099508 Break this problem into two subproblems by setting (x + -1.916666667) equal to 2.945099508 and -2.945099508.Subproblem 1
x + -1.916666667 = 2.945099508 Simplifying x + -1.916666667 = 2.945099508 Reorder the terms: -1.916666667 + x = 2.945099508 Solving -1.916666667 + x = 2.945099508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = 2.945099508 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = 2.945099508 + 1.916666667 x = 2.945099508 + 1.916666667 Combine like terms: 2.945099508 + 1.916666667 = 4.861766175 x = 4.861766175 Simplifying x = 4.861766175Subproblem 2
x + -1.916666667 = -2.945099508 Simplifying x + -1.916666667 = -2.945099508 Reorder the terms: -1.916666667 + x = -2.945099508 Solving -1.916666667 + x = -2.945099508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = -2.945099508 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = -2.945099508 + 1.916666667 x = -2.945099508 + 1.916666667 Combine like terms: -2.945099508 + 1.916666667 = -1.028432841 x = -1.028432841 Simplifying x = -1.028432841Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.861766175, -1.028432841}
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