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Simplifying 5x3 + 2x2 + -1x = 0 Reorder the terms: -1x + 2x2 + 5x3 = 0 Solving -1x + 2x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 2x + 5x2) = 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 '(-1 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + 5x2 = 0 Solving -1 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.4x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.4x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.4x + x2 = 0 + 0.2 0.4x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.4x + x2 = 0.2 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + 0.4x + x2 = 0.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + 0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
x + 0.2 = 0.489897949 Simplifying x + 0.2 = 0.489897949 Reorder the terms: 0.2 + x = 0.489897949 Solving 0.2 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.489897949 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.489897949 + -0.2 x = 0.489897949 + -0.2 Combine like terms: 0.489897949 + -0.2 = 0.289897949 x = 0.289897949 Simplifying x = 0.289897949Subproblem 2
x + 0.2 = -0.489897949 Simplifying x + 0.2 = -0.489897949 Reorder the terms: 0.2 + x = -0.489897949 Solving 0.2 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.489897949 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.489897949 + -0.2 x = -0.489897949 + -0.2 Combine like terms: -0.489897949 + -0.2 = -0.689897949 x = -0.689897949 Simplifying x = -0.689897949Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.289897949, -0.689897949}Solution
x = {0, 0.289897949, -0.689897949}
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