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Simplifying 2x2 + 6x + 149 = x2 + -22x + 121 Reorder the terms: 149 + 6x + 2x2 = x2 + -22x + 121 Reorder the terms: 149 + 6x + 2x2 = 121 + -22x + x2 Solving 149 + 6x + 2x2 = 121 + -22x + x2 Solving for variable 'x'. Reorder the terms: 149 + -121 + 6x + 22x + 2x2 + -1x2 = 121 + -22x + x2 + -121 + 22x + -1x2 Combine like terms: 149 + -121 = 28 28 + 6x + 22x + 2x2 + -1x2 = 121 + -22x + x2 + -121 + 22x + -1x2 Combine like terms: 6x + 22x = 28x 28 + 28x + 2x2 + -1x2 = 121 + -22x + x2 + -121 + 22x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 28 + 28x + 1x2 = 121 + -22x + x2 + -121 + 22x + -1x2 Reorder the terms: 28 + 28x + 1x2 = 121 + -121 + -22x + 22x + x2 + -1x2 Combine like terms: 121 + -121 = 0 28 + 28x + 1x2 = 0 + -22x + 22x + x2 + -1x2 28 + 28x + 1x2 = -22x + 22x + x2 + -1x2 Combine like terms: -22x + 22x = 0 28 + 28x + 1x2 = 0 + x2 + -1x2 28 + 28x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 28 + 28x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 28x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + 28x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 28x + x2 = 0 + -28 28x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 28x + x2 = -28 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -28 + 196 Reorder the terms: 196 + 28x + x2 = -28 + 196 Combine like terms: -28 + 196 = 168 196 + 28x + x2 = 168 Factor a perfect square on the left side: (x + 14)(x + 14) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (x + 14) equal to 12.961481397 and -12.961481397.Subproblem 1
x + 14 = 12.961481397 Simplifying x + 14 = 12.961481397 Reorder the terms: 14 + x = 12.961481397 Solving 14 + x = 12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 12.961481397 + -14 Combine like terms: 14 + -14 = 0 0 + x = 12.961481397 + -14 x = 12.961481397 + -14 Combine like terms: 12.961481397 + -14 = -1.038518603 x = -1.038518603 Simplifying x = -1.038518603Subproblem 2
x + 14 = -12.961481397 Simplifying x + 14 = -12.961481397 Reorder the terms: 14 + x = -12.961481397 Solving 14 + x = -12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -12.961481397 + -14 Combine like terms: 14 + -14 = 0 0 + x = -12.961481397 + -14 x = -12.961481397 + -14 Combine like terms: -12.961481397 + -14 = -26.961481397 x = -26.961481397 Simplifying x = -26.961481397Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.038518603, -26.961481397}
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