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Simplifying 30x3 + -216x2 + -196x = 0 Reorder the terms: -196x + -216x2 + 30x3 = 0 Solving -196x + -216x2 + 30x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-98 + -108x + 15x2) = 0 Ignore the factor 2.Subproblem 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 '(-98 + -108x + 15x2)' equal to zero and attempt to solve: Simplifying -98 + -108x + 15x2 = 0 Solving -98 + -108x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -6.533333333 + -7.2x + x2 = 0 Move the constant term to the right: Add '6.533333333' to each side of the equation. -6.533333333 + -7.2x + 6.533333333 + x2 = 0 + 6.533333333 Reorder the terms: -6.533333333 + 6.533333333 + -7.2x + x2 = 0 + 6.533333333 Combine like terms: -6.533333333 + 6.533333333 = 0.000000000 0.000000000 + -7.2x + x2 = 0 + 6.533333333 -7.2x + x2 = 0 + 6.533333333 Combine like terms: 0 + 6.533333333 = 6.533333333 -7.2x + x2 = 6.533333333 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = 6.533333333 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 6.533333333 + 12.96 Combine like terms: 6.533333333 + 12.96 = 19.493333333 12.96 + -7.2x + x2 = 19.493333333 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 19.493333333 Calculate the square root of the right side: 4.415125517 Break this problem into two subproblems by setting (x + -3.6) equal to 4.415125517 and -4.415125517.Subproblem 1
x + -3.6 = 4.415125517 Simplifying x + -3.6 = 4.415125517 Reorder the terms: -3.6 + x = 4.415125517 Solving -3.6 + x = 4.415125517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 4.415125517 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 4.415125517 + 3.6 x = 4.415125517 + 3.6 Combine like terms: 4.415125517 + 3.6 = 8.015125517 x = 8.015125517 Simplifying x = 8.015125517Subproblem 2
x + -3.6 = -4.415125517 Simplifying x + -3.6 = -4.415125517 Reorder the terms: -3.6 + x = -4.415125517 Solving -3.6 + x = -4.415125517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -4.415125517 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -4.415125517 + 3.6 x = -4.415125517 + 3.6 Combine like terms: -4.415125517 + 3.6 = -0.815125517 x = -0.815125517 Simplifying x = -0.815125517Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.015125517, -0.815125517}Solution
x = {0, 8.015125517, -0.815125517}
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