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Simplifying 85 = x2 + 7x Reorder the terms: 85 = 7x + x2 Solving 85 = 7x + x2 Solving for variable 'x'. Reorder the terms: 85 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 85 + -7x + -1x2 = 0 + x2 + -1x2 85 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 85 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -85 + 7x + x2 = 0 Move the constant term to the right: Add '85' to each side of the equation. -85 + 7x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 7x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 7x + x2 = 0 + 85 7x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 7x + x2 = 85 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 = 85 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 85 + 12.25 Combine like terms: 85 + 12.25 = 97.25 12.25 + 7x + x2 = 97.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 97.25 Calculate the square root of the right side: 9.861541462 Break this problem into two subproblems by setting (x + 3.5) equal to 9.861541462 and -9.861541462.Subproblem 1
x + 3.5 = 9.861541462 Simplifying x + 3.5 = 9.861541462 Reorder the terms: 3.5 + x = 9.861541462 Solving 3.5 + x = 9.861541462 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 = 9.861541462 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.861541462 + -3.5 x = 9.861541462 + -3.5 Combine like terms: 9.861541462 + -3.5 = 6.361541462 x = 6.361541462 Simplifying x = 6.361541462Subproblem 2
x + 3.5 = -9.861541462 Simplifying x + 3.5 = -9.861541462 Reorder the terms: 3.5 + x = -9.861541462 Solving 3.5 + x = -9.861541462 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 = -9.861541462 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.861541462 + -3.5 x = -9.861541462 + -3.5 Combine like terms: -9.861541462 + -3.5 = -13.361541462 x = -13.361541462 Simplifying x = -13.361541462Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.361541462, -13.361541462}
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