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Simplifying 0 = x2 + -7x + -312 Reorder the terms: 0 = -312 + -7x + x2 Solving 0 = -312 + -7x + x2 Solving for variable 'x'. Combine like terms: 0 + 312 = 312 312 + 7x + -1x2 = -312 + -7x + x2 + 312 + 7x + -1x2 Reorder the terms: 312 + 7x + -1x2 = -312 + 312 + -7x + 7x + x2 + -1x2 Combine like terms: -312 + 312 = 0 312 + 7x + -1x2 = 0 + -7x + 7x + x2 + -1x2 312 + 7x + -1x2 = -7x + 7x + x2 + -1x2 Combine like terms: -7x + 7x = 0 312 + 7x + -1x2 = 0 + x2 + -1x2 312 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 312 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -312 + -7x + x2 = 0 Move the constant term to the right: Add '312' to each side of the equation. -312 + -7x + 312 + x2 = 0 + 312 Reorder the terms: -312 + 312 + -7x + x2 = 0 + 312 Combine like terms: -312 + 312 = 0 0 + -7x + x2 = 0 + 312 -7x + x2 = 0 + 312 Combine like terms: 0 + 312 = 312 -7x + x2 = 312 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 = 312 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 312 + 12.25 Combine like terms: 312 + 12.25 = 324.25 12.25 + -7x + x2 = 324.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 324.25 Calculate the square root of the right side: 18.006943105 Break this problem into two subproblems by setting (x + -3.5) equal to 18.006943105 and -18.006943105.Subproblem 1
x + -3.5 = 18.006943105 Simplifying x + -3.5 = 18.006943105 Reorder the terms: -3.5 + x = 18.006943105 Solving -3.5 + x = 18.006943105 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 = 18.006943105 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 18.006943105 + 3.5 x = 18.006943105 + 3.5 Combine like terms: 18.006943105 + 3.5 = 21.506943105 x = 21.506943105 Simplifying x = 21.506943105Subproblem 2
x + -3.5 = -18.006943105 Simplifying x + -3.5 = -18.006943105 Reorder the terms: -3.5 + x = -18.006943105 Solving -3.5 + x = -18.006943105 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 = -18.006943105 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -18.006943105 + 3.5 x = -18.006943105 + 3.5 Combine like terms: -18.006943105 + 3.5 = -14.506943105 x = -14.506943105 Simplifying x = -14.506943105Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.506943105, -14.506943105}
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