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Simplifying x2 + -6x + 21 = 180 Reorder the terms: 21 + -6x + x2 = 180 Solving 21 + -6x + x2 = 180 Solving for variable 'x'. Reorder the terms: 21 + -180 + -6x + x2 = 180 + -180 Combine like terms: 21 + -180 = -159 -159 + -6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -159 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '159' to each side of the equation. -159 + -6x + 159 + x2 = 0 + 159 Reorder the terms: -159 + 159 + -6x + x2 = 0 + 159 Combine like terms: -159 + 159 = 0 0 + -6x + x2 = 0 + 159 -6x + x2 = 0 + 159 Combine like terms: 0 + 159 = 159 -6x + x2 = 159 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 159 + 9 Reorder the terms: 9 + -6x + x2 = 159 + 9 Combine like terms: 159 + 9 = 168 9 + -6x + x2 = 168 Factor a perfect square on the left side: (x + -3)(x + -3) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (x + -3) equal to 12.961481397 and -12.961481397.Subproblem 1
x + -3 = 12.961481397 Simplifying x + -3 = 12.961481397 Reorder the terms: -3 + x = 12.961481397 Solving -3 + x = 12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 12.961481397 + 3 Combine like terms: -3 + 3 = 0 0 + x = 12.961481397 + 3 x = 12.961481397 + 3 Combine like terms: 12.961481397 + 3 = 15.961481397 x = 15.961481397 Simplifying x = 15.961481397Subproblem 2
x + -3 = -12.961481397 Simplifying x + -3 = -12.961481397 Reorder the terms: -3 + x = -12.961481397 Solving -3 + x = -12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -12.961481397 + 3 Combine like terms: -3 + 3 = 0 0 + x = -12.961481397 + 3 x = -12.961481397 + 3 Combine like terms: -12.961481397 + 3 = -9.961481397 x = -9.961481397 Simplifying x = -9.961481397Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.961481397, -9.961481397}
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