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Simplifying 3x(x + 10) + 4(x + 20) + 5x = 185 + -3x Reorder the terms: 3x(10 + x) + 4(x + 20) + 5x = 185 + -3x (10 * 3x + x * 3x) + 4(x + 20) + 5x = 185 + -3x (30x + 3x2) + 4(x + 20) + 5x = 185 + -3x Reorder the terms: 30x + 3x2 + 4(20 + x) + 5x = 185 + -3x 30x + 3x2 + (20 * 4 + x * 4) + 5x = 185 + -3x 30x + 3x2 + (80 + 4x) + 5x = 185 + -3x Reorder the terms: 80 + 30x + 4x + 5x + 3x2 = 185 + -3x Combine like terms: 30x + 4x = 34x 80 + 34x + 5x + 3x2 = 185 + -3x Combine like terms: 34x + 5x = 39x 80 + 39x + 3x2 = 185 + -3x Solving 80 + 39x + 3x2 = 185 + -3x Solving for variable 'x'. Reorder the terms: 80 + -185 + 39x + 3x + 3x2 = 185 + -3x + -185 + 3x Combine like terms: 80 + -185 = -105 -105 + 39x + 3x + 3x2 = 185 + -3x + -185 + 3x Combine like terms: 39x + 3x = 42x -105 + 42x + 3x2 = 185 + -3x + -185 + 3x Reorder the terms: -105 + 42x + 3x2 = 185 + -185 + -3x + 3x Combine like terms: 185 + -185 = 0 -105 + 42x + 3x2 = 0 + -3x + 3x -105 + 42x + 3x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -105 + 42x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-35 + 14x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-35 + 14x + x2)' equal to zero and attempt to solve: Simplifying -35 + 14x + x2 = 0 Solving -35 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 14x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 14x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 14x + x2 = 0 + 35 14x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 14x + x2 = 35 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 35 + 49 Reorder the terms: 49 + 14x + x2 = 35 + 49 Combine like terms: 35 + 49 = 84 49 + 14x + x2 = 84 Factor a perfect square on the left side: (x + 7)(x + 7) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + 7) equal to 9.16515139 and -9.16515139.Subproblem 1
x + 7 = 9.16515139 Simplifying x + 7 = 9.16515139 Reorder the terms: 7 + x = 9.16515139 Solving 7 + x = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 9.16515139 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.16515139 + -7 x = 9.16515139 + -7 Combine like terms: 9.16515139 + -7 = 2.16515139 x = 2.16515139 Simplifying x = 2.16515139Subproblem 2
x + 7 = -9.16515139 Simplifying x + 7 = -9.16515139 Reorder the terms: 7 + x = -9.16515139 Solving 7 + x = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -9.16515139 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.16515139 + -7 x = -9.16515139 + -7 Combine like terms: -9.16515139 + -7 = -16.16515139 x = -16.16515139 Simplifying x = -16.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.16515139, -16.16515139}Solution
x = {2.16515139, -16.16515139}
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