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Simplifying x(x + 3) = -7(3x + 3) Reorder the terms: x(3 + x) = -7(3x + 3) (3 * x + x * x) = -7(3x + 3) (3x + x2) = -7(3x + 3) Reorder the terms: 3x + x2 = -7(3 + 3x) 3x + x2 = (3 * -7 + 3x * -7) 3x + x2 = (-21 + -21x) Solving 3x + x2 = -21 + -21x Solving for variable 'x'. Reorder the terms: 21 + 3x + 21x + x2 = -21 + -21x + 21 + 21x Combine like terms: 3x + 21x = 24x 21 + 24x + x2 = -21 + -21x + 21 + 21x Reorder the terms: 21 + 24x + x2 = -21 + 21 + -21x + 21x Combine like terms: -21 + 21 = 0 21 + 24x + x2 = 0 + -21x + 21x 21 + 24x + x2 = -21x + 21x Combine like terms: -21x + 21x = 0 21 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 24x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 24x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 24x + x2 = 0 + -21 24x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 24x + x2 = -21 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -21 + 144 Reorder the terms: 144 + 24x + x2 = -21 + 144 Combine like terms: -21 + 144 = 123 144 + 24x + x2 = 123 Factor a perfect square on the left side: (x + 12)(x + 12) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (x + 12) equal to 11.090536506 and -11.090536506.Subproblem 1
x + 12 = 11.090536506 Simplifying x + 12 = 11.090536506 Reorder the terms: 12 + x = 11.090536506 Solving 12 + x = 11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 11.090536506 + -12 Combine like terms: 12 + -12 = 0 0 + x = 11.090536506 + -12 x = 11.090536506 + -12 Combine like terms: 11.090536506 + -12 = -0.909463494 x = -0.909463494 Simplifying x = -0.909463494Subproblem 2
x + 12 = -11.090536506 Simplifying x + 12 = -11.090536506 Reorder the terms: 12 + x = -11.090536506 Solving 12 + x = -11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -11.090536506 + -12 Combine like terms: 12 + -12 = 0 0 + x = -11.090536506 + -12 x = -11.090536506 + -12 Combine like terms: -11.090536506 + -12 = -23.090536506 x = -23.090536506 Simplifying x = -23.090536506Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.909463494, -23.090536506}
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