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Simplifying 100 = x2 + -7x + -108 Reorder the terms: 100 = -108 + -7x + x2 Solving 100 = -108 + -7x + x2 Solving for variable 'x'. Combine like terms: 100 + 108 = 208 208 + 7x + -1x2 = -108 + -7x + x2 + 108 + 7x + -1x2 Reorder the terms: 208 + 7x + -1x2 = -108 + 108 + -7x + 7x + x2 + -1x2 Combine like terms: -108 + 108 = 0 208 + 7x + -1x2 = 0 + -7x + 7x + x2 + -1x2 208 + 7x + -1x2 = -7x + 7x + x2 + -1x2 Combine like terms: -7x + 7x = 0 208 + 7x + -1x2 = 0 + x2 + -1x2 208 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 208 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -208 + -7x + x2 = 0 Move the constant term to the right: Add '208' to each side of the equation. -208 + -7x + 208 + x2 = 0 + 208 Reorder the terms: -208 + 208 + -7x + x2 = 0 + 208 Combine like terms: -208 + 208 = 0 0 + -7x + x2 = 0 + 208 -7x + x2 = 0 + 208 Combine like terms: 0 + 208 = 208 -7x + x2 = 208 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 = 208 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 208 + 12.25 Combine like terms: 208 + 12.25 = 220.25 12.25 + -7x + x2 = 220.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 220.25 Calculate the square root of the right side: 14.84082208 Break this problem into two subproblems by setting (x + -3.5) equal to 14.84082208 and -14.84082208.Subproblem 1
x + -3.5 = 14.84082208 Simplifying x + -3.5 = 14.84082208 Reorder the terms: -3.5 + x = 14.84082208 Solving -3.5 + x = 14.84082208 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 = 14.84082208 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 14.84082208 + 3.5 x = 14.84082208 + 3.5 Combine like terms: 14.84082208 + 3.5 = 18.34082208 x = 18.34082208 Simplifying x = 18.34082208Subproblem 2
x + -3.5 = -14.84082208 Simplifying x + -3.5 = -14.84082208 Reorder the terms: -3.5 + x = -14.84082208 Solving -3.5 + x = -14.84082208 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 = -14.84082208 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -14.84082208 + 3.5 x = -14.84082208 + 3.5 Combine like terms: -14.84082208 + 3.5 = -11.34082208 x = -11.34082208 Simplifying x = -11.34082208Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.34082208, -11.34082208}
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