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Simplifying 500x4 = -100x3 + 31500x2 Reorder the terms: 500x4 = 31500x2 + -100x3 Solving 500x4 = 31500x2 + -100x3 Solving for variable 'x'. Reorder the terms: -31500x2 + 100x3 + 500x4 = 31500x2 + -100x3 + -31500x2 + 100x3 Reorder the terms: -31500x2 + 100x3 + 500x4 = 31500x2 + -31500x2 + -100x3 + 100x3 Combine like terms: 31500x2 + -31500x2 = 0 -31500x2 + 100x3 + 500x4 = 0 + -100x3 + 100x3 -31500x2 + 100x3 + 500x4 = -100x3 + 100x3 Combine like terms: -100x3 + 100x3 = 0 -31500x2 + 100x3 + 500x4 = 0 Factor out the Greatest Common Factor (GCF), '100x2'. 100x2(-315 + x + 5x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-315 + x + 5x2)' equal to zero and attempt to solve: Simplifying -315 + x + 5x2 = 0 Solving -315 + x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -63 + 0.2x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 0.2x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 0.2x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 0.2x + x2 = 0 + 63 0.2x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 0.2x + x2 = 63 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. 0.2x + 0.25 + x2 = 63 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 63 + 0.25 Combine like terms: 63 + 0.25 = 63.25 0.25 + 0.2x + x2 = 63.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + 0.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + 0.5 = 7.95298686 Simplifying x + 0.5 = 7.95298686 Reorder the terms: 0.5 + x = 7.95298686 Solving 0.5 + x = 7.95298686 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 = 7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.95298686 + -0.5 x = 7.95298686 + -0.5 Combine like terms: 7.95298686 + -0.5 = 7.45298686 x = 7.45298686 Simplifying x = 7.45298686Subproblem 2
x + 0.5 = -7.95298686 Simplifying x + 0.5 = -7.95298686 Reorder the terms: 0.5 + x = -7.95298686 Solving 0.5 + x = -7.95298686 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 = -7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.95298686 + -0.5 x = -7.95298686 + -0.5 Combine like terms: -7.95298686 + -0.5 = -8.45298686 x = -8.45298686 Simplifying x = -8.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.45298686, -8.45298686}Solution
x = {0, 7.45298686, -8.45298686}
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