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Simplifying 15x4 + 54x3 + 21x2 = 0 Reorder the terms: 21x2 + 54x3 + 15x4 = 0 Solving 21x2 + 54x3 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(7 + 18x + 5x2) = 0 Ignore the factor 3.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 '(7 + 18x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + 18x + 5x2 = 0 Solving 7 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 3.6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 3.6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 3.6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 3.6x + x2 = 0 + -1.4 3.6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 3.6x + x2 = -1.4 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = -1.4 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = -1.4 + 3.24 Combine like terms: -1.4 + 3.24 = 1.84 3.24 + 3.6x + x2 = 1.84 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + 1.8) equal to 1.356465997 and -1.356465997.Subproblem 1
x + 1.8 = 1.356465997 Simplifying x + 1.8 = 1.356465997 Reorder the terms: 1.8 + x = 1.356465997 Solving 1.8 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 1.356465997 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 1.356465997 + -1.8 x = 1.356465997 + -1.8 Combine like terms: 1.356465997 + -1.8 = -0.443534003 x = -0.443534003 Simplifying x = -0.443534003Subproblem 2
x + 1.8 = -1.356465997 Simplifying x + 1.8 = -1.356465997 Reorder the terms: 1.8 + x = -1.356465997 Solving 1.8 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -1.356465997 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -1.356465997 + -1.8 x = -1.356465997 + -1.8 Combine like terms: -1.356465997 + -1.8 = -3.156465997 x = -3.156465997 Simplifying x = -3.156465997Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.443534003, -3.156465997}Solution
x = {0, -0.443534003, -3.156465997}
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