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Simplifying 10x3 + -15x2 + 3x = 0 Reorder the terms: 3x + -15x2 + 10x3 = 0 Solving 3x + -15x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + -15x + 10x2) = 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 '(3 + -15x + 10x2)' equal to zero and attempt to solve: Simplifying 3 + -15x + 10x2 = 0 Solving 3 + -15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -1.5x + -0.3 + x2 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + -1.5x + x2 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -1.5x + x2 = 0 + -0.3 -1.5x + x2 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 -1.5x + x2 = -0.3 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.3 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.3 + 0.5625 Combine like terms: -0.3 + 0.5625 = 0.2625 0.5625 + -1.5x + x2 = 0.2625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.2625 Calculate the square root of the right side: 0.512347538 Break this problem into two subproblems by setting (x + -0.75) equal to 0.512347538 and -0.512347538.Subproblem 1
x + -0.75 = 0.512347538 Simplifying x + -0.75 = 0.512347538 Reorder the terms: -0.75 + x = 0.512347538 Solving -0.75 + x = 0.512347538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.512347538 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.512347538 + 0.75 x = 0.512347538 + 0.75 Combine like terms: 0.512347538 + 0.75 = 1.262347538 x = 1.262347538 Simplifying x = 1.262347538Subproblem 2
x + -0.75 = -0.512347538 Simplifying x + -0.75 = -0.512347538 Reorder the terms: -0.75 + x = -0.512347538 Solving -0.75 + x = -0.512347538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.512347538 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.512347538 + 0.75 x = -0.512347538 + 0.75 Combine like terms: -0.512347538 + 0.75 = 0.237652462 x = 0.237652462 Simplifying x = 0.237652462Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.262347538, 0.237652462}Solution
x = {0, 1.262347538, 0.237652462}
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