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Simplifying x2 + 12x + 3x + 20 = 180 Reorder the terms: 20 + 12x + 3x + x2 = 180 Combine like terms: 12x + 3x = 15x 20 + 15x + x2 = 180 Solving 20 + 15x + x2 = 180 Solving for variable 'x'. Reorder the terms: 20 + -180 + 15x + x2 = 180 + -180 Combine like terms: 20 + -180 = -160 -160 + 15x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -160 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + 15x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 15x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 15x + x2 = 0 + 160 15x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 15x + x2 = 160 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 160 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 160 + 56.25 Combine like terms: 160 + 56.25 = 216.25 56.25 + 15x + x2 = 216.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 216.25 Calculate the square root of the right side: 14.70544117 Break this problem into two subproblems by setting (x + 7.5) equal to 14.70544117 and -14.70544117.Subproblem 1
x + 7.5 = 14.70544117 Simplifying x + 7.5 = 14.70544117 Reorder the terms: 7.5 + x = 14.70544117 Solving 7.5 + x = 14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 14.70544117 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 14.70544117 + -7.5 x = 14.70544117 + -7.5 Combine like terms: 14.70544117 + -7.5 = 7.20544117 x = 7.20544117 Simplifying x = 7.20544117Subproblem 2
x + 7.5 = -14.70544117 Simplifying x + 7.5 = -14.70544117 Reorder the terms: 7.5 + x = -14.70544117 Solving 7.5 + x = -14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -14.70544117 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -14.70544117 + -7.5 x = -14.70544117 + -7.5 Combine like terms: -14.70544117 + -7.5 = -22.20544117 x = -22.20544117 Simplifying x = -22.20544117Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.20544117, -22.20544117}
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