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Simplifying 4 + 3x(5x + 14) = -39x + -8 Reorder the terms: 4 + 3x(14 + 5x) = -39x + -8 4 + (14 * 3x + 5x * 3x) = -39x + -8 4 + (42x + 15x2) = -39x + -8 Reorder the terms: 4 + 42x + 15x2 = -8 + -39x Solving 4 + 42x + 15x2 = -8 + -39x Solving for variable 'x'. Reorder the terms: 4 + 8 + 42x + 39x + 15x2 = -8 + -39x + 8 + 39x Combine like terms: 4 + 8 = 12 12 + 42x + 39x + 15x2 = -8 + -39x + 8 + 39x Combine like terms: 42x + 39x = 81x 12 + 81x + 15x2 = -8 + -39x + 8 + 39x Reorder the terms: 12 + 81x + 15x2 = -8 + 8 + -39x + 39x Combine like terms: -8 + 8 = 0 12 + 81x + 15x2 = 0 + -39x + 39x 12 + 81x + 15x2 = -39x + 39x Combine like terms: -39x + 39x = 0 12 + 81x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 27x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 27x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 27x + 5x2 = 0 Solving 4 + 27x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 5.4x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 5.4x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 5.4x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 5.4x + x2 = 0 + -0.8 5.4x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 5.4x + x2 = -0.8 The x term is 5.4x. Take half its coefficient (2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. 5.4x + 7.29 + x2 = -0.8 + 7.29 Reorder the terms: 7.29 + 5.4x + x2 = -0.8 + 7.29 Combine like terms: -0.8 + 7.29 = 6.49 7.29 + 5.4x + x2 = 6.49 Factor a perfect square on the left side: (x + 2.7)(x + 2.7) = 6.49 Calculate the square root of the right side: 2.547547841 Break this problem into two subproblems by setting (x + 2.7) equal to 2.547547841 and -2.547547841.Subproblem 1
x + 2.7 = 2.547547841 Simplifying x + 2.7 = 2.547547841 Reorder the terms: 2.7 + x = 2.547547841 Solving 2.7 + x = 2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = 2.547547841 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 2.547547841 + -2.7 x = 2.547547841 + -2.7 Combine like terms: 2.547547841 + -2.7 = -0.152452159 x = -0.152452159 Simplifying x = -0.152452159Subproblem 2
x + 2.7 = -2.547547841 Simplifying x + 2.7 = -2.547547841 Reorder the terms: 2.7 + x = -2.547547841 Solving 2.7 + x = -2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = -2.547547841 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -2.547547841 + -2.7 x = -2.547547841 + -2.7 Combine like terms: -2.547547841 + -2.7 = -5.247547841 x = -5.247547841 Simplifying x = -5.247547841Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.152452159, -5.247547841}Solution
x = {-0.152452159, -5.247547841}
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