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Simplifying x(5x + 12) = 12 Reorder the terms: x(12 + 5x) = 12 (12 * x + 5x * x) = 12 (12x + 5x2) = 12 Solving 12x + 5x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 12x + 5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 2.4x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 2.4x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 2.4x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 2.4x + x2 = 0 + 2.4 2.4x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 2.4x + x2 = 2.4 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 = 2.4 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 2.4 + 1.44 Combine like terms: 2.4 + 1.44 = 3.84 1.44 + 2.4x + x2 = 3.84 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (x + 1.2) equal to 1.959591794 and -1.959591794.Subproblem 1
x + 1.2 = 1.959591794 Simplifying x + 1.2 = 1.959591794 Reorder the terms: 1.2 + x = 1.959591794 Solving 1.2 + x = 1.959591794 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 = 1.959591794 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.959591794 + -1.2 x = 1.959591794 + -1.2 Combine like terms: 1.959591794 + -1.2 = 0.759591794 x = 0.759591794 Simplifying x = 0.759591794Subproblem 2
x + 1.2 = -1.959591794 Simplifying x + 1.2 = -1.959591794 Reorder the terms: 1.2 + x = -1.959591794 Solving 1.2 + x = -1.959591794 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 = -1.959591794 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.959591794 + -1.2 x = -1.959591794 + -1.2 Combine like terms: -1.959591794 + -1.2 = -3.159591794 x = -3.159591794 Simplifying x = -3.159591794Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.759591794, -3.159591794}
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