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Simplifying 5x3 + -34x2 + -21x = 0 Reorder the terms: -21x + -34x2 + 5x3 = 0 Solving -21x + -34x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-21 + -34x + 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 '(-21 + -34x + 5x2)' equal to zero and attempt to solve: Simplifying -21 + -34x + 5x2 = 0 Solving -21 + -34x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -6.8x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -6.8x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -6.8x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -6.8x + x2 = 0 + 4.2 -6.8x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -6.8x + x2 = 4.2 The x term is -6.8x. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8x + 11.56 + x2 = 4.2 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = 4.2 + 11.56 Combine like terms: 4.2 + 11.56 = 15.76 11.56 + -6.8x + x2 = 15.76 Factor a perfect square on the left side: (x + -3.4)(x + -3.4) = 15.76 Calculate the square root of the right side: 3.969886648 Break this problem into two subproblems by setting (x + -3.4) equal to 3.969886648 and -3.969886648.Subproblem 1
x + -3.4 = 3.969886648 Simplifying x + -3.4 = 3.969886648 Reorder the terms: -3.4 + x = 3.969886648 Solving -3.4 + x = 3.969886648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 3.969886648 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 3.969886648 + 3.4 x = 3.969886648 + 3.4 Combine like terms: 3.969886648 + 3.4 = 7.369886648 x = 7.369886648 Simplifying x = 7.369886648Subproblem 2
x + -3.4 = -3.969886648 Simplifying x + -3.4 = -3.969886648 Reorder the terms: -3.4 + x = -3.969886648 Solving -3.4 + x = -3.969886648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -3.969886648 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -3.969886648 + 3.4 x = -3.969886648 + 3.4 Combine like terms: -3.969886648 + 3.4 = -0.569886648 x = -0.569886648 Simplifying x = -0.569886648Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.369886648, -0.569886648}Solution
x = {0, 7.369886648, -0.569886648}
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