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Simplifying 5x2 + 12x + -144 = 0 Reorder the terms: -144 + 12x + 5x2 = 0 Solving -144 + 12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -28.8 + 2.4x + x2 = 0 Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + 2.4x + 28.8 + x2 = 0 + 28.8 Reorder the terms: -28.8 + 28.8 + 2.4x + x2 = 0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + 2.4x + x2 = 0 + 28.8 2.4x + x2 = 0 + 28.8 Combine like terms: 0 + 28.8 = 28.8 2.4x + x2 = 28.8 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 = 28.8 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 28.8 + 1.44 Combine like terms: 28.8 + 1.44 = 30.24 1.44 + 2.4x + x2 = 30.24 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 30.24 Calculate the square root of the right side: 5.499090834 Break this problem into two subproblems by setting (x + 1.2) equal to 5.499090834 and -5.499090834.Subproblem 1
x + 1.2 = 5.499090834 Simplifying x + 1.2 = 5.499090834 Reorder the terms: 1.2 + x = 5.499090834 Solving 1.2 + x = 5.499090834 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 = 5.499090834 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 5.499090834 + -1.2 x = 5.499090834 + -1.2 Combine like terms: 5.499090834 + -1.2 = 4.299090834 x = 4.299090834 Simplifying x = 4.299090834Subproblem 2
x + 1.2 = -5.499090834 Simplifying x + 1.2 = -5.499090834 Reorder the terms: 1.2 + x = -5.499090834 Solving 1.2 + x = -5.499090834 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 = -5.499090834 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -5.499090834 + -1.2 x = -5.499090834 + -1.2 Combine like terms: -5.499090834 + -1.2 = -6.699090834 x = -6.699090834 Simplifying x = -6.699090834Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.299090834, -6.699090834}
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