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Simplifying x2 + 6x + 95 = 180 Reorder the terms: 95 + 6x + x2 = 180 Solving 95 + 6x + x2 = 180 Solving for variable 'x'. Reorder the terms: 95 + -180 + 6x + x2 = 180 + -180 Combine like terms: 95 + -180 = -85 -85 + 6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -85 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 6x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 6x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 6x + x2 = 0 + 85 6x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 6x + x2 = 85 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 = 85 + 9 Reorder the terms: 9 + 6x + x2 = 85 + 9 Combine like terms: 85 + 9 = 94 9 + 6x + x2 = 94 Factor a perfect square on the left side: (x + 3)(x + 3) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + 3) equal to 9.695359715 and -9.695359715.Subproblem 1
x + 3 = 9.695359715 Simplifying x + 3 = 9.695359715 Reorder the terms: 3 + x = 9.695359715 Solving 3 + x = 9.695359715 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 = 9.695359715 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.695359715 + -3 x = 9.695359715 + -3 Combine like terms: 9.695359715 + -3 = 6.695359715 x = 6.695359715 Simplifying x = 6.695359715Subproblem 2
x + 3 = -9.695359715 Simplifying x + 3 = -9.695359715 Reorder the terms: 3 + x = -9.695359715 Solving 3 + x = -9.695359715 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 = -9.695359715 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.695359715 + -3 x = -9.695359715 + -3 Combine like terms: -9.695359715 + -3 = -12.695359715 x = -12.695359715 Simplifying x = -12.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.695359715, -12.695359715}
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