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Simplifying x2 + 12x + 9 = 144 Reorder the terms: 9 + 12x + x2 = 144 Solving 9 + 12x + x2 = 144 Solving for variable 'x'. Reorder the terms: 9 + -144 + 12x + x2 = 144 + -144 Combine like terms: 9 + -144 = -135 -135 + 12x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -135 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + 12x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + 12x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 12x + x2 = 0 + 135 12x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 12x + x2 = 135 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 135 + 36 Reorder the terms: 36 + 12x + x2 = 135 + 36 Combine like terms: 135 + 36 = 171 36 + 12x + x2 = 171 Factor a perfect square on the left side: (x + 6)(x + 6) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + 6) equal to 13.076696831 and -13.076696831.Subproblem 1
x + 6 = 13.076696831 Simplifying x + 6 = 13.076696831 Reorder the terms: 6 + x = 13.076696831 Solving 6 + x = 13.076696831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 13.076696831 + -6 Combine like terms: 6 + -6 = 0 0 + x = 13.076696831 + -6 x = 13.076696831 + -6 Combine like terms: 13.076696831 + -6 = 7.076696831 x = 7.076696831 Simplifying x = 7.076696831Subproblem 2
x + 6 = -13.076696831 Simplifying x + 6 = -13.076696831 Reorder the terms: 6 + x = -13.076696831 Solving 6 + x = -13.076696831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -13.076696831 + -6 Combine like terms: 6 + -6 = 0 0 + x = -13.076696831 + -6 x = -13.076696831 + -6 Combine like terms: -13.076696831 + -6 = -19.076696831 x = -19.076696831 Simplifying x = -19.076696831Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.076696831, -19.076696831}
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