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Simplifying 5x2(7x2 + x + 1) = 0 Reorder the terms: 5x2(1 + x + 7x2) = 0 (1 * 5x2 + x * 5x2 + 7x2 * 5x2) = 0 (5x2 + 5x3 + 35x4) = 0 Solving 5x2 + 5x3 + 35x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(1 + x + 7x2) = 0 Ignore the factor 5.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 + x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + x + 7x2 = 0 Solving 1 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.1428571429x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.1428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + -0.1428571429 0.1428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.1428571429x + x2 = -0.1428571429 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. 0.1428571429x + 0.25 + x2 = -0.1428571429 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = -0.1428571429 + 0.25 Combine like terms: -0.1428571429 + 0.25 = 0.1071428571 0.25 + 0.1428571429x + x2 = 0.1071428571 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.1071428571 Calculate the square root of the right side: 0.327326835 Break this problem into two subproblems by setting (x + 0.5) equal to 0.327326835 and -0.327326835.Subproblem 1
x + 0.5 = 0.327326835 Simplifying x + 0.5 = 0.327326835 Reorder the terms: 0.5 + x = 0.327326835 Solving 0.5 + x = 0.327326835 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 = 0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.327326835 + -0.5 x = 0.327326835 + -0.5 Combine like terms: 0.327326835 + -0.5 = -0.172673165 x = -0.172673165 Simplifying x = -0.172673165Subproblem 2
x + 0.5 = -0.327326835 Simplifying x + 0.5 = -0.327326835 Reorder the terms: 0.5 + x = -0.327326835 Solving 0.5 + x = -0.327326835 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 = -0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.327326835 + -0.5 x = -0.327326835 + -0.5 Combine like terms: -0.327326835 + -0.5 = -0.827326835 x = -0.827326835 Simplifying x = -0.827326835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.172673165, -0.827326835}Solution
x = {0, -0.172673165, -0.827326835}
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