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Simplifying 3x2 + 18x + -25 = 0 Reorder the terms: -25 + 18x + 3x2 = 0 Solving -25 + 18x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.333333333 + 6x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + 6x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + 6x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + 6x + x2 = 0 + 8.333333333 6x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 6x + x2 = 8.333333333 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 8.333333333 + 9 Reorder the terms: 9 + 6x + x2 = 8.333333333 + 9 Combine like terms: 8.333333333 + 9 = 17.333333333 9 + 6x + x2 = 17.333333333 Factor a perfect square on the left side: (x + 3)(x + 3) = 17.333333333 Calculate the square root of the right side: 4.163331999 Break this problem into two subproblems by setting (x + 3) equal to 4.163331999 and -4.163331999.Subproblem 1
x + 3 = 4.163331999 Simplifying x + 3 = 4.163331999 Reorder the terms: 3 + x = 4.163331999 Solving 3 + x = 4.163331999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.163331999 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.163331999 + -3 x = 4.163331999 + -3 Combine like terms: 4.163331999 + -3 = 1.163331999 x = 1.163331999 Simplifying x = 1.163331999Subproblem 2
x + 3 = -4.163331999 Simplifying x + 3 = -4.163331999 Reorder the terms: 3 + x = -4.163331999 Solving 3 + x = -4.163331999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.163331999 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.163331999 + -3 x = -4.163331999 + -3 Combine like terms: -4.163331999 + -3 = -7.163331999 x = -7.163331999 Simplifying x = -7.163331999Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.163331999, -7.163331999}
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