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Simplifying 10x3 + x2 + -640x = 0 Reorder the terms: -640x + x2 + 10x3 = 0 Solving -640x + x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-640 + x + 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 '(-640 + x + 10x2)' equal to zero and attempt to solve: Simplifying -640 + x + 10x2 = 0 Solving -640 + x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -64 + 0.1x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 0.1x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 0.1x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 0.1x + x2 = 0 + 64 0.1x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 0.1x + x2 = 64 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1x + 0.25 + x2 = 64 + 0.25 Reorder the terms: 0.25 + 0.1x + x2 = 64 + 0.25 Combine like terms: 64 + 0.25 = 64.25 0.25 + 0.1x + x2 = 64.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + 0.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + 0.5 = 8.015609771 Simplifying x + 0.5 = 8.015609771 Reorder the terms: 0.5 + x = 8.015609771 Solving 0.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 8.015609771 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.015609771 + -0.5 x = 8.015609771 + -0.5 Combine like terms: 8.015609771 + -0.5 = 7.515609771 x = 7.515609771 Simplifying x = 7.515609771Subproblem 2
x + 0.5 = -8.015609771 Simplifying x + 0.5 = -8.015609771 Reorder the terms: 0.5 + x = -8.015609771 Solving 0.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -8.015609771 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.015609771 + -0.5 x = -8.015609771 + -0.5 Combine like terms: -8.015609771 + -0.5 = -8.515609771 x = -8.515609771 Simplifying x = -8.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.515609771, -8.515609771}Solution
x = {0, 7.515609771, -8.515609771}
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