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Simplifying 3x2 + 10 + 15x + 120 = 180 Reorder the terms: 10 + 120 + 15x + 3x2 = 180 Combine like terms: 10 + 120 = 130 130 + 15x + 3x2 = 180 Solving 130 + 15x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: 130 + -180 + 15x + 3x2 = 180 + -180 Combine like terms: 130 + -180 = -50 -50 + 15x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -50 + 15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + 5x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + 5x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + 5x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + 5x + x2 = 0 + 16.66666667 5x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 5x + x2 = 16.66666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 16.66666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 16.66666667 + 6.25 Combine like terms: 16.66666667 + 6.25 = 22.91666667 6.25 + 5x + x2 = 22.91666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 22.91666667 Calculate the square root of the right side: 4.787135539 Break this problem into two subproblems by setting (x + 2.5) equal to 4.787135539 and -4.787135539.Subproblem 1
x + 2.5 = 4.787135539 Simplifying x + 2.5 = 4.787135539 Reorder the terms: 2.5 + x = 4.787135539 Solving 2.5 + x = 4.787135539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.787135539 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.787135539 + -2.5 x = 4.787135539 + -2.5 Combine like terms: 4.787135539 + -2.5 = 2.287135539 x = 2.287135539 Simplifying x = 2.287135539Subproblem 2
x + 2.5 = -4.787135539 Simplifying x + 2.5 = -4.787135539 Reorder the terms: 2.5 + x = -4.787135539 Solving 2.5 + x = -4.787135539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.787135539 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.787135539 + -2.5 x = -4.787135539 + -2.5 Combine like terms: -4.787135539 + -2.5 = -7.287135539 x = -7.287135539 Simplifying x = -7.287135539Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.287135539, -7.287135539}
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