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Simplifying 0 = x2 + 7x + -860 Reorder the terms: 0 = -860 + 7x + x2 Solving 0 = -860 + 7x + x2 Solving for variable 'x'. Combine like terms: 0 + 860 = 860 860 + -7x + -1x2 = -860 + 7x + x2 + 860 + -7x + -1x2 Reorder the terms: 860 + -7x + -1x2 = -860 + 860 + 7x + -7x + x2 + -1x2 Combine like terms: -860 + 860 = 0 860 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2 860 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 860 + -7x + -1x2 = 0 + x2 + -1x2 860 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 860 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -860 + 7x + x2 = 0 Move the constant term to the right: Add '860' to each side of the equation. -860 + 7x + 860 + x2 = 0 + 860 Reorder the terms: -860 + 860 + 7x + x2 = 0 + 860 Combine like terms: -860 + 860 = 0 0 + 7x + x2 = 0 + 860 7x + x2 = 0 + 860 Combine like terms: 0 + 860 = 860 7x + x2 = 860 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 = 860 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 860 + 12.25 Combine like terms: 860 + 12.25 = 872.25 12.25 + 7x + x2 = 872.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 872.25 Calculate the square root of the right side: 29.533878851 Break this problem into two subproblems by setting (x + 3.5) equal to 29.533878851 and -29.533878851.Subproblem 1
x + 3.5 = 29.533878851 Simplifying x + 3.5 = 29.533878851 Reorder the terms: 3.5 + x = 29.533878851 Solving 3.5 + x = 29.533878851 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 = 29.533878851 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 29.533878851 + -3.5 x = 29.533878851 + -3.5 Combine like terms: 29.533878851 + -3.5 = 26.033878851 x = 26.033878851 Simplifying x = 26.033878851Subproblem 2
x + 3.5 = -29.533878851 Simplifying x + 3.5 = -29.533878851 Reorder the terms: 3.5 + x = -29.533878851 Solving 3.5 + x = -29.533878851 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 = -29.533878851 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -29.533878851 + -3.5 x = -29.533878851 + -3.5 Combine like terms: -29.533878851 + -3.5 = -33.033878851 x = -33.033878851 Simplifying x = -33.033878851Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.033878851, -33.033878851}
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