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Simplifying 28x = 5x3 + 3x2 Reorder the terms: 28x = 3x2 + 5x3 Solving 28x = 3x2 + 5x3 Solving for variable 'x'. Reorder the terms: 28x + -3x2 + -5x3 = 3x2 + -3x2 + 5x3 + -5x3 Combine like terms: 3x2 + -3x2 = 0 28x + -3x2 + -5x3 = 0 + 5x3 + -5x3 28x + -3x2 + -5x3 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 28x + -3x2 + -5x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(28 + -3x + -5x2) = 0Subproblem 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 '(28 + -3x + -5x2)' equal to zero and attempt to solve: Simplifying 28 + -3x + -5x2 = 0 Solving 28 + -3x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.6 + 0.6x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 0.6x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 0.6x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 0.6x + x2 = 0 + 5.6 0.6x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 0.6x + x2 = 5.6 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 5.6 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 5.6 + 0.09 Combine like terms: 5.6 + 0.09 = 5.69 0.09 + 0.6x + x2 = 5.69 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 5.69 Calculate the square root of the right side: 2.385372088 Break this problem into two subproblems by setting (x + 0.3) equal to 2.385372088 and -2.385372088.Subproblem 1
x + 0.3 = 2.385372088 Simplifying x + 0.3 = 2.385372088 Reorder the terms: 0.3 + x = 2.385372088 Solving 0.3 + x = 2.385372088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 2.385372088 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.385372088 + -0.3 x = 2.385372088 + -0.3 Combine like terms: 2.385372088 + -0.3 = 2.085372088 x = 2.085372088 Simplifying x = 2.085372088Subproblem 2
x + 0.3 = -2.385372088 Simplifying x + 0.3 = -2.385372088 Reorder the terms: 0.3 + x = -2.385372088 Solving 0.3 + x = -2.385372088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -2.385372088 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.385372088 + -0.3 x = -2.385372088 + -0.3 Combine like terms: -2.385372088 + -0.3 = -2.685372088 x = -2.685372088 Simplifying x = -2.685372088Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.085372088, -2.685372088}Solution
x = {0, 2.085372088, -2.685372088}
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