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Simplifying 0 = x2 + x + -189 Reorder the terms: 0 = -189 + x + x2 Solving 0 = -189 + x + x2 Solving for variable 'x'. Combine like terms: 0 + 189 = 189 189 + -1x + -1x2 = -189 + x + x2 + 189 + -1x + -1x2 Reorder the terms: 189 + -1x + -1x2 = -189 + 189 + x + -1x + x2 + -1x2 Combine like terms: -189 + 189 = 0 189 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2 189 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 189 + -1x + -1x2 = 0 + x2 + -1x2 189 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 189 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -189 + x + x2 = 0 Move the constant term to the right: Add '189' to each side of the equation. -189 + x + 189 + x2 = 0 + 189 Reorder the terms: -189 + 189 + x + x2 = 0 + 189 Combine like terms: -189 + 189 = 0 0 + x + x2 = 0 + 189 x + x2 = 0 + 189 Combine like terms: 0 + 189 = 189 x + x2 = 189 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 189 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 189 + 0.25 Combine like terms: 189 + 0.25 = 189.25 1.25 + x2 = 189.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 189.25 Calculate the square root of the right side: 13.756816492 Break this problem into two subproblems by setting (x + 0.5) equal to 13.756816492 and -13.756816492.Subproblem 1
x + 0.5 = 13.756816492 Simplifying x + 0.5 = 13.756816492 Reorder the terms: 0.5 + x = 13.756816492 Solving 0.5 + x = 13.756816492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.756816492 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.756816492 + -0.5 x = 13.756816492 + -0.5 Combine like terms: 13.756816492 + -0.5 = 13.256816492 x = 13.256816492 Simplifying x = 13.256816492Subproblem 2
x + 0.5 = -13.756816492 Simplifying x + 0.5 = -13.756816492 Reorder the terms: 0.5 + x = -13.756816492 Solving 0.5 + x = -13.756816492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.756816492 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.756816492 + -0.5 x = -13.756816492 + -0.5 Combine like terms: -13.756816492 + -0.5 = -14.256816492 x = -14.256816492 Simplifying x = -14.256816492Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.256816492, -14.256816492}
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