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Simplifying -15x4 + 45x2 = 6 Reorder the terms: 45x2 + -15x4 = 6 Solving 45x2 + -15x4 = 6 Solving for variable 'x'. Reorder the terms: -6 + 45x2 + -15x4 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 45x2 + -15x4 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 15x2 + -5x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 15x2 + -5x4)' equal to zero and attempt to solve: Simplifying -2 + 15x2 + -5x4 = 0 Solving -2 + 15x2 + -5x4 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.4 + -3x2 + x4 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -3x2 + -0.4 + x4 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -3x2 + x4 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -3x2 + x4 = 0 + -0.4 -3x2 + x4 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -3x2 + x4 = -0.4 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = -0.4 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = -0.4 + 2.25 Combine like terms: -0.4 + 2.25 = 1.85 2.25 + -3x2 + x4 = 1.85 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 1.85 Calculate the square root of the right side: 1.360147051 Break this problem into two subproblems by setting (x2 + -1.5) equal to 1.360147051 and -1.360147051.Subproblem 1
x2 + -1.5 = 1.360147051 Simplifying x2 + -1.5 = 1.360147051 Reorder the terms: -1.5 + x2 = 1.360147051 Solving -1.5 + x2 = 1.360147051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 1.360147051 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 1.360147051 + 1.5 x2 = 1.360147051 + 1.5 Combine like terms: 1.360147051 + 1.5 = 2.860147051 x2 = 2.860147051 Simplifying x2 = 2.860147051 Take the square root of each side: x = {-1.691196929, 1.691196929}Subproblem 2
x2 + -1.5 = -1.360147051 Simplifying x2 + -1.5 = -1.360147051 Reorder the terms: -1.5 + x2 = -1.360147051 Solving -1.5 + x2 = -1.360147051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -1.360147051 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -1.360147051 + 1.5 x2 = -1.360147051 + 1.5 Combine like terms: -1.360147051 + 1.5 = 0.139852949 x2 = 0.139852949 Simplifying x2 = 0.139852949 Take the square root of each side: x = {-0.373969182, 0.373969182}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.691196929, 1.691196929, -0.373969182, 0.373969182}Solution
x = {-1.691196929, 1.691196929, -0.373969182, 0.373969182}
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