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Simplifying 4x5 + -225x = 61x3 Reorder the terms: -225x + 4x5 = 61x3 Solving -225x + 4x5 = 61x3 Solving for variable 'x'. Reorder the terms: -225x + -61x3 + 4x5 = 61x3 + -61x3 Combine like terms: 61x3 + -61x3 = 0 -225x + -61x3 + 4x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-225 + -61x2 + 4x4) = 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 '(-225 + -61x2 + 4x4)' equal to zero and attempt to solve: Simplifying -225 + -61x2 + 4x4 = 0 Solving -225 + -61x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -56.25 + -15.25x2 + x4 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + -15.25x2 + 56.25 + x4 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + -15.25x2 + x4 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + -15.25x2 + x4 = 0 + 56.25 -15.25x2 + x4 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 -15.25x2 + x4 = 56.25 The x term is -15.25x2. Take half its coefficient (-7.625). Square it (58.140625) and add it to both sides. Add '58.140625' to each side of the equation. -15.25x2 + 58.140625 + x4 = 56.25 + 58.140625 Reorder the terms: 58.140625 + -15.25x2 + x4 = 56.25 + 58.140625 Combine like terms: 56.25 + 58.140625 = 114.390625 58.140625 + -15.25x2 + x4 = 114.390625 Factor a perfect square on the left side: (x2 + -7.625)(x2 + -7.625) = 114.390625 Calculate the square root of the right side: 10.6953553 Break this problem into two subproblems by setting (x2 + -7.625) equal to 10.6953553 and -10.6953553.Subproblem 1
x2 + -7.625 = 10.6953553 Simplifying x2 + -7.625 = 10.6953553 Reorder the terms: -7.625 + x2 = 10.6953553 Solving -7.625 + x2 = 10.6953553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x2 = 10.6953553 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x2 = 10.6953553 + 7.625 x2 = 10.6953553 + 7.625 Combine like terms: 10.6953553 + 7.625 = 18.3203553 x2 = 18.3203553 Simplifying x2 = 18.3203553 Take the square root of each side: x = {-4.280228417, 4.280228417}Subproblem 2
x2 + -7.625 = -10.6953553 Simplifying x2 + -7.625 = -10.6953553 Reorder the terms: -7.625 + x2 = -10.6953553 Solving -7.625 + x2 = -10.6953553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x2 = -10.6953553 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x2 = -10.6953553 + 7.625 x2 = -10.6953553 + 7.625 Combine like terms: -10.6953553 + 7.625 = -3.0703553 x2 = -3.0703553 Simplifying x2 = -3.0703553 Reorder the terms: 3.0703553 + x2 = -3.0703553 + 3.0703553 Combine like terms: -3.0703553 + 3.0703553 = 0.0000000 3.0703553 + x2 = 0.0000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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