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Simplifying 15x4 + 21x3 + 3x2 = 0 Reorder the terms: 3x2 + 21x3 + 15x4 = 0 Solving 3x2 + 21x3 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(1 + 7x + 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 '(1 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + 7x + 5x2 = 0 Solving 1 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 1.4x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.4x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.4x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.4x + x2 = 0 + -0.2 1.4x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.4x + x2 = -0.2 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -0.2 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -0.2 + 0.49 Combine like terms: -0.2 + 0.49 = 0.29 0.49 + 1.4x + x2 = 0.29 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x + 0.7) equal to 0.538516481 and -0.538516481.Subproblem 1
x + 0.7 = 0.538516481 Simplifying x + 0.7 = 0.538516481 Reorder the terms: 0.7 + x = 0.538516481 Solving 0.7 + x = 0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 0.538516481 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.538516481 + -0.7 x = 0.538516481 + -0.7 Combine like terms: 0.538516481 + -0.7 = -0.161483519 x = -0.161483519 Simplifying x = -0.161483519Subproblem 2
x + 0.7 = -0.538516481 Simplifying x + 0.7 = -0.538516481 Reorder the terms: 0.7 + x = -0.538516481 Solving 0.7 + x = -0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -0.538516481 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.538516481 + -0.7 x = -0.538516481 + -0.7 Combine like terms: -0.538516481 + -0.7 = -1.238516481 x = -1.238516481 Simplifying x = -1.238516481Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.161483519, -1.238516481}Solution
x = {0, -0.161483519, -1.238516481}
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