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Simplifying 0 = x2 + 7x + -5974 Reorder the terms: 0 = -5974 + 7x + x2 Solving 0 = -5974 + 7x + x2 Solving for variable 'x'. Combine like terms: 0 + 5974 = 5974 5974 + -7x + -1x2 = -5974 + 7x + x2 + 5974 + -7x + -1x2 Reorder the terms: 5974 + -7x + -1x2 = -5974 + 5974 + 7x + -7x + x2 + -1x2 Combine like terms: -5974 + 5974 = 0 5974 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2 5974 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 5974 + -7x + -1x2 = 0 + x2 + -1x2 5974 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5974 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5974 + 7x + x2 = 0 Move the constant term to the right: Add '5974' to each side of the equation. -5974 + 7x + 5974 + x2 = 0 + 5974 Reorder the terms: -5974 + 5974 + 7x + x2 = 0 + 5974 Combine like terms: -5974 + 5974 = 0 0 + 7x + x2 = 0 + 5974 7x + x2 = 0 + 5974 Combine like terms: 0 + 5974 = 5974 7x + x2 = 5974 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 5974 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 5974 + 12.25 Combine like terms: 5974 + 12.25 = 5986.25 12.25 + 7x + x2 = 5986.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 5986.25 Calculate the square root of the right side: 77.370860148 Break this problem into two subproblems by setting (x + 3.5) equal to 77.370860148 and -77.370860148.Subproblem 1
x + 3.5 = 77.370860148 Simplifying x + 3.5 = 77.370860148 Reorder the terms: 3.5 + x = 77.370860148 Solving 3.5 + x = 77.370860148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 77.370860148 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 77.370860148 + -3.5 x = 77.370860148 + -3.5 Combine like terms: 77.370860148 + -3.5 = 73.870860148 x = 73.870860148 Simplifying x = 73.870860148Subproblem 2
x + 3.5 = -77.370860148 Simplifying x + 3.5 = -77.370860148 Reorder the terms: 3.5 + x = -77.370860148 Solving 3.5 + x = -77.370860148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -77.370860148 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -77.370860148 + -3.5 x = -77.370860148 + -3.5 Combine like terms: -77.370860148 + -3.5 = -80.870860148 x = -80.870860148 Simplifying x = -80.870860148Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.870860148, -80.870860148}
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