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Simplifying 10x3 + -290x2 + 620x = 0 Reorder the terms: 620x + -290x2 + 10x3 = 0 Solving 620x + -290x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(62 + -29x + x2) = 0 Ignore the factor 10.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 '(62 + -29x + x2)' equal to zero and attempt to solve: Simplifying 62 + -29x + x2 = 0 Solving 62 + -29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-62' to each side of the equation. 62 + -29x + -62 + x2 = 0 + -62 Reorder the terms: 62 + -62 + -29x + x2 = 0 + -62 Combine like terms: 62 + -62 = 0 0 + -29x + x2 = 0 + -62 -29x + x2 = 0 + -62 Combine like terms: 0 + -62 = -62 -29x + x2 = -62 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -62 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -62 + 210.25 Combine like terms: -62 + 210.25 = 148.25 210.25 + -29x + x2 = 148.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 148.25 Calculate the square root of the right side: 12.175795662 Break this problem into two subproblems by setting (x + -14.5) equal to 12.175795662 and -12.175795662.Subproblem 1
x + -14.5 = 12.175795662 Simplifying x + -14.5 = 12.175795662 Reorder the terms: -14.5 + x = 12.175795662 Solving -14.5 + x = 12.175795662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 12.175795662 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 12.175795662 + 14.5 x = 12.175795662 + 14.5 Combine like terms: 12.175795662 + 14.5 = 26.675795662 x = 26.675795662 Simplifying x = 26.675795662Subproblem 2
x + -14.5 = -12.175795662 Simplifying x + -14.5 = -12.175795662 Reorder the terms: -14.5 + x = -12.175795662 Solving -14.5 + x = -12.175795662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -12.175795662 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -12.175795662 + 14.5 x = -12.175795662 + 14.5 Combine like terms: -12.175795662 + 14.5 = 2.324204338 x = 2.324204338 Simplifying x = 2.324204338Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.675795662, 2.324204338}Solution
x = {0, 26.675795662, 2.324204338}
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