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Simplifying 10x3 + 5x2 + -3x = 0 Reorder the terms: -3x + 5x2 + 10x3 = 0 Solving -3x + 5x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + 5x + 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 + 5x + 10x2)' equal to zero and attempt to solve: Simplifying -3 + 5x + 10x2 = 0 Solving -3 + 5x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.5x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.5x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.5x + x2 = 0 + 0.3 0.5x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.5x + x2 = 0.3 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.3 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.3 + 0.0625 Combine like terms: 0.3 + 0.0625 = 0.3625 0.0625 + 0.5x + x2 = 0.3625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.3625 Calculate the square root of the right side: 0.602079729 Break this problem into two subproblems by setting (x + 0.25) equal to 0.602079729 and -0.602079729.Subproblem 1
x + 0.25 = 0.602079729 Simplifying x + 0.25 = 0.602079729 Reorder the terms: 0.25 + x = 0.602079729 Solving 0.25 + x = 0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.602079729 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.602079729 + -0.25 x = 0.602079729 + -0.25 Combine like terms: 0.602079729 + -0.25 = 0.352079729 x = 0.352079729 Simplifying x = 0.352079729Subproblem 2
x + 0.25 = -0.602079729 Simplifying x + 0.25 = -0.602079729 Reorder the terms: 0.25 + x = -0.602079729 Solving 0.25 + x = -0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.602079729 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.602079729 + -0.25 x = -0.602079729 + -0.25 Combine like terms: -0.602079729 + -0.25 = -0.852079729 x = -0.852079729 Simplifying x = -0.852079729Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.352079729, -0.852079729}Solution
x = {0, 0.352079729, -0.852079729}
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