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Simplifying 7x + 28 = x2 Reorder the terms: 28 + 7x = x2 Solving 28 + 7x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 28 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + -7x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -7x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -7x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -7x + x2 = 0 + 28 -7x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -7x + x2 = 28 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 = 28 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 28 + 12.25 Combine like terms: 28 + 12.25 = 40.25 12.25 + -7x + x2 = 40.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -3.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -3.5 = 6.34428877 Simplifying x + -3.5 = 6.34428877 Reorder the terms: -3.5 + x = 6.34428877 Solving -3.5 + x = 6.34428877 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 = 6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.34428877 + 3.5 x = 6.34428877 + 3.5 Combine like terms: 6.34428877 + 3.5 = 9.84428877 x = 9.84428877 Simplifying x = 9.84428877Subproblem 2
x + -3.5 = -6.34428877 Simplifying x + -3.5 = -6.34428877 Reorder the terms: -3.5 + x = -6.34428877 Solving -3.5 + x = -6.34428877 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 = -6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.34428877 + 3.5 x = -6.34428877 + 3.5 Combine like terms: -6.34428877 + 3.5 = -2.84428877 x = -2.84428877 Simplifying x = -2.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.84428877, -2.84428877}
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