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Simplifying 0 = -0.12x2 + 12x + 720 Reorder the terms: 0 = 720 + 12x + -0.12x2 Solving 0 = 720 + 12x + -0.12x2 Solving for variable 'x'. Combine like terms: 0 + -720 = -720 -720 + -12x + 0.12x2 = 720 + 12x + -0.12x2 + -720 + -12x + 0.12x2 Reorder the terms: -720 + -12x + 0.12x2 = 720 + -720 + 12x + -12x + -0.12x2 + 0.12x2 Combine like terms: 720 + -720 = 0 -720 + -12x + 0.12x2 = 0 + 12x + -12x + -0.12x2 + 0.12x2 -720 + -12x + 0.12x2 = 12x + -12x + -0.12x2 + 0.12x2 Combine like terms: 12x + -12x = 0 -720 + -12x + 0.12x2 = 0 + -0.12x2 + 0.12x2 -720 + -12x + 0.12x2 = -0.12x2 + 0.12x2 Combine like terms: -0.12x2 + 0.12x2 = 0.00 -720 + -12x + 0.12x2 = 0.00 Begin completing the square. Divide all terms by 0.12 the coefficient of the squared term: Divide each side by '0.12'. -6000 + -100x + x2 = 0 Move the constant term to the right: Add '6000' to each side of the equation. -6000 + -100x + 6000 + x2 = 0 + 6000 Reorder the terms: -6000 + 6000 + -100x + x2 = 0 + 6000 Combine like terms: -6000 + 6000 = 0 0 + -100x + x2 = 0 + 6000 -100x + x2 = 0 + 6000 Combine like terms: 0 + 6000 = 6000 -100x + x2 = 6000 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 6000 + 2500 Reorder the terms: 2500 + -100x + x2 = 6000 + 2500 Combine like terms: 6000 + 2500 = 8500 2500 + -100x + x2 = 8500 Factor a perfect square on the left side: (x + -50)(x + -50) = 8500 Calculate the square root of the right side: 92.195444573 Break this problem into two subproblems by setting (x + -50) equal to 92.195444573 and -92.195444573.Subproblem 1
x + -50 = 92.195444573 Simplifying x + -50 = 92.195444573 Reorder the terms: -50 + x = 92.195444573 Solving -50 + x = 92.195444573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 92.195444573 + 50 Combine like terms: -50 + 50 = 0 0 + x = 92.195444573 + 50 x = 92.195444573 + 50 Combine like terms: 92.195444573 + 50 = 142.195444573 x = 142.195444573 Simplifying x = 142.195444573Subproblem 2
x + -50 = -92.195444573 Simplifying x + -50 = -92.195444573 Reorder the terms: -50 + x = -92.195444573 Solving -50 + x = -92.195444573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -92.195444573 + 50 Combine like terms: -50 + 50 = 0 0 + x = -92.195444573 + 50 x = -92.195444573 + 50 Combine like terms: -92.195444573 + 50 = -42.195444573 x = -42.195444573 Simplifying x = -42.195444573Solution
The solution to the problem is based on the solutions from the subproblems. x = {142.195444573, -42.195444573}
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