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Simplifying 9x2 + 12x + 125 = 324 Reorder the terms: 125 + 12x + 9x2 = 324 Solving 125 + 12x + 9x2 = 324 Solving for variable 'x'. Reorder the terms: 125 + -324 + 12x + 9x2 = 324 + -324 Combine like terms: 125 + -324 = -199 -199 + 12x + 9x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -199 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -22.11111111 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '22.11111111' to each side of the equation. -22.11111111 + 1.333333333x + 22.11111111 + x2 = 0 + 22.11111111 Reorder the terms: -22.11111111 + 22.11111111 + 1.333333333x + x2 = 0 + 22.11111111 Combine like terms: -22.11111111 + 22.11111111 = 0.00000000 0.00000000 + 1.333333333x + x2 = 0 + 22.11111111 1.333333333x + x2 = 0 + 22.11111111 Combine like terms: 0 + 22.11111111 = 22.11111111 1.333333333x + x2 = 22.11111111 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 22.11111111 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 22.11111111 + 0.4444444442 Combine like terms: 22.11111111 + 0.4444444442 = 22.5555555542 0.4444444442 + 1.333333333x + x2 = 22.5555555542 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 22.5555555542 Calculate the square root of the right side: 4.749268949 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 4.749268949 and -4.749268949.Subproblem 1
x + 0.6666666665 = 4.749268949 Simplifying x + 0.6666666665 = 4.749268949 Reorder the terms: 0.6666666665 + x = 4.749268949 Solving 0.6666666665 + x = 4.749268949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 4.749268949 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 4.749268949 + -0.6666666665 x = 4.749268949 + -0.6666666665 Combine like terms: 4.749268949 + -0.6666666665 = 4.0826022825 x = 4.0826022825 Simplifying x = 4.0826022825Subproblem 2
x + 0.6666666665 = -4.749268949 Simplifying x + 0.6666666665 = -4.749268949 Reorder the terms: 0.6666666665 + x = -4.749268949 Solving 0.6666666665 + x = -4.749268949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -4.749268949 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -4.749268949 + -0.6666666665 x = -4.749268949 + -0.6666666665 Combine like terms: -4.749268949 + -0.6666666665 = -5.4159356155 x = -5.4159356155 Simplifying x = -5.4159356155Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.0826022825, -5.4159356155}
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