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Simplifying 15x3 + 57x2 + 12x = 0 Reorder the terms: 12x + 57x2 + 15x3 = 0 Solving 12x + 57x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(4 + 19x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(4 + 19x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 19x + 5x2 = 0 Solving 4 + 19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 3.8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 3.8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 3.8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 3.8x + x2 = 0 + -0.8 3.8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 3.8x + x2 = -0.8 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = -0.8 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = -0.8 + 3.61 Combine like terms: -0.8 + 3.61 = 2.81 3.61 + 3.8x + x2 = 2.81 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 2.81 Calculate the square root of the right side: 1.676305461 Break this problem into two subproblems by setting (x + 1.9) equal to 1.676305461 and -1.676305461.Subproblem 1
x + 1.9 = 1.676305461 Simplifying x + 1.9 = 1.676305461 Reorder the terms: 1.9 + x = 1.676305461 Solving 1.9 + x = 1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 1.676305461 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 1.676305461 + -1.9 x = 1.676305461 + -1.9 Combine like terms: 1.676305461 + -1.9 = -0.223694539 x = -0.223694539 Simplifying x = -0.223694539Subproblem 2
x + 1.9 = -1.676305461 Simplifying x + 1.9 = -1.676305461 Reorder the terms: 1.9 + x = -1.676305461 Solving 1.9 + x = -1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -1.676305461 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -1.676305461 + -1.9 x = -1.676305461 + -1.9 Combine like terms: -1.676305461 + -1.9 = -3.576305461 x = -3.576305461 Simplifying x = -3.576305461Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.223694539, -3.576305461}Solution
x = {0, -0.223694539, -3.576305461}
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