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Simplifying (x2 + 1) + (4x + 3) + (2x2 + 3x + -2) = 360 Reorder the terms: (1 + x2) + (4x + 3) + (2x2 + 3x + -2) = 360 Remove parenthesis around (1 + x2) 1 + x2 + (4x + 3) + (2x2 + 3x + -2) = 360 Reorder the terms: 1 + x2 + (3 + 4x) + (2x2 + 3x + -2) = 360 Remove parenthesis around (3 + 4x) 1 + x2 + 3 + 4x + (2x2 + 3x + -2) = 360 Reorder the terms: 1 + x2 + 3 + 4x + (-2 + 3x + 2x2) = 360 Remove parenthesis around (-2 + 3x + 2x2) 1 + x2 + 3 + 4x + -2 + 3x + 2x2 = 360 Reorder the terms: 1 + 3 + -2 + 4x + 3x + x2 + 2x2 = 360 Combine like terms: 1 + 3 = 4 4 + -2 + 4x + 3x + x2 + 2x2 = 360 Combine like terms: 4 + -2 = 2 2 + 4x + 3x + x2 + 2x2 = 360 Combine like terms: 4x + 3x = 7x 2 + 7x + x2 + 2x2 = 360 Combine like terms: x2 + 2x2 = 3x2 2 + 7x + 3x2 = 360 Solving 2 + 7x + 3x2 = 360 Solving for variable 'x'. Reorder the terms: 2 + -360 + 7x + 3x2 = 360 + -360 Combine like terms: 2 + -360 = -358 -358 + 7x + 3x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -358 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -119.3333333 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '119.3333333' to each side of the equation. -119.3333333 + 2.333333333x + 119.3333333 + x2 = 0 + 119.3333333 Reorder the terms: -119.3333333 + 119.3333333 + 2.333333333x + x2 = 0 + 119.3333333 Combine like terms: -119.3333333 + 119.3333333 = 0.0000000 0.0000000 + 2.333333333x + x2 = 0 + 119.3333333 2.333333333x + x2 = 0 + 119.3333333 Combine like terms: 0 + 119.3333333 = 119.3333333 2.333333333x + x2 = 119.3333333 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 119.3333333 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 119.3333333 + 1.361111112 Combine like terms: 119.3333333 + 1.361111112 = 120.694444412 1.361111112 + 2.333333333x + x2 = 120.694444412 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 120.694444412 Calculate the square root of the right side: 10.98610233 Break this problem into two subproblems by setting (x + 1.166666667) equal to 10.98610233 and -10.98610233.Subproblem 1
x + 1.166666667 = 10.98610233 Simplifying x + 1.166666667 = 10.98610233 Reorder the terms: 1.166666667 + x = 10.98610233 Solving 1.166666667 + x = 10.98610233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 10.98610233 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 10.98610233 + -1.166666667 x = 10.98610233 + -1.166666667 Combine like terms: 10.98610233 + -1.166666667 = 9.819435663 x = 9.819435663 Simplifying x = 9.819435663Subproblem 2
x + 1.166666667 = -10.98610233 Simplifying x + 1.166666667 = -10.98610233 Reorder the terms: 1.166666667 + x = -10.98610233 Solving 1.166666667 + x = -10.98610233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -10.98610233 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -10.98610233 + -1.166666667 x = -10.98610233 + -1.166666667 Combine like terms: -10.98610233 + -1.166666667 = -12.152768997 x = -12.152768997 Simplifying x = -12.152768997Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.819435663, -12.152768997}
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