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Simplifying 0(6 + -1) + 1((3x + -3) + -1(-2)) + -1x((-1x + 1) + -1(4)) = 29 Combine like terms: 6 + -1 = 5 0(5) + 1((3x + -3) + -1(-2)) + -1x((-1x + 1) + -1(4)) = 29 Multiply 0 * 5 0 + 1((3x + -3) + -1(-2)) + -1x((-1x + 1) + -1(4)) = 29 Anything times zero is zero. 0 + 1((3x + -3) + -1(-2)) + -1x((-1x + 1) + -1(4)) = 29 Reorder the terms: 0 + 1((-3 + 3x) + -1(-2)) + -1x((-1x + 1) + -1(4)) = 29 Remove parenthesis around (-3 + 3x) 0 + 1(-3 + 3x + -1(-2)) + -1x((-1x + 1) + -1(4)) = 29 Multiply -1 * -2 0 + 1(-3 + 3x + 2) + -1x((-1x + 1) + -1(4)) = 29 Reorder the terms: 0 + 1(-3 + 2 + 3x) + -1x((-1x + 1) + -1(4)) = 29 Combine like terms: -3 + 2 = -1 0 + 1(-1 + 3x) + -1x((-1x + 1) + -1(4)) = 29 0 + (-1 * 1 + 3x * 1) + -1x((-1x + 1) + -1(4)) = 29 0 + (-1 + 3x) + -1x((-1x + 1) + -1(4)) = 29 Reorder the terms: 0 + -1 + 3x + -1x((1 + -1x) + -1(4)) = 29 Remove parenthesis around (1 + -1x) 0 + -1 + 3x + -1x(1 + -1x + -1(4)) = 29 Multiply -1 * 4 0 + -1 + 3x + -1x(1 + -1x + -4) = 29 Reorder the terms: 0 + -1 + 3x + -1x(1 + -4 + -1x) = 29 Combine like terms: 1 + -4 = -3 0 + -1 + 3x + -1x(-3 + -1x) = 29 0 + -1 + 3x + (-3 * -1x + -1x * -1x) = 29 0 + -1 + 3x + (3x + 1x2) = 29 Combine like terms: 0 + -1 = -1 -1 + 3x + 3x + 1x2 = 29 Combine like terms: 3x + 3x = 6x -1 + 6x + 1x2 = 29 Solving -1 + 6x + 1x2 = 29 Solving for variable 'x'. Reorder the terms: -1 + -29 + 6x + 1x2 = 29 + -29 Combine like terms: -1 + -29 = -30 -30 + 6x + 1x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -30 + 6x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 6x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 6x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 6x + x2 = 0 + 30 6x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 6x + x2 = 30 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 = 30 + 9 Reorder the terms: 9 + 6x + x2 = 30 + 9 Combine like terms: 30 + 9 = 39 9 + 6x + x2 = 39 Factor a perfect square on the left side: (x + 3)(x + 3) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 3) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 3 = 6.244997998 Simplifying x + 3 = 6.244997998 Reorder the terms: 3 + x = 6.244997998 Solving 3 + x = 6.244997998 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 = 6.244997998 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.244997998 + -3 x = 6.244997998 + -3 Combine like terms: 6.244997998 + -3 = 3.244997998 x = 3.244997998 Simplifying x = 3.244997998Subproblem 2
x + 3 = -6.244997998 Simplifying x + 3 = -6.244997998 Reorder the terms: 3 + x = -6.244997998 Solving 3 + x = -6.244997998 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 = -6.244997998 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.244997998 + -3 x = -6.244997998 + -3 Combine like terms: -6.244997998 + -3 = -9.244997998 x = -9.244997998 Simplifying x = -9.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.244997998, -9.244997998}
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