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Simplifying 4x3 + 6x2 + -196x = 0 Reorder the terms: -196x + 6x2 + 4x3 = 0 Solving -196x + 6x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-98 + 3x + 2x2) = 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 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -98 + 3x + 2x2 = 0 Solving -98 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -49 + 1.5x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 1.5x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 1.5x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 1.5x + x2 = 0 + 49 1.5x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 1.5x + x2 = 49 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 49 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 49 + 0.5625 Combine like terms: 49 + 0.5625 = 49.5625 0.5625 + 1.5x + x2 = 49.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 49.5625 Calculate the square root of the right side: 7.04006392 Break this problem into two subproblems by setting (x + 0.75) equal to 7.04006392 and -7.04006392.Subproblem 1
x + 0.75 = 7.04006392 Simplifying x + 0.75 = 7.04006392 Reorder the terms: 0.75 + x = 7.04006392 Solving 0.75 + x = 7.04006392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 7.04006392 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.04006392 + -0.75 x = 7.04006392 + -0.75 Combine like terms: 7.04006392 + -0.75 = 6.29006392 x = 6.29006392 Simplifying x = 6.29006392Subproblem 2
x + 0.75 = -7.04006392 Simplifying x + 0.75 = -7.04006392 Reorder the terms: 0.75 + x = -7.04006392 Solving 0.75 + x = -7.04006392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -7.04006392 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.04006392 + -0.75 x = -7.04006392 + -0.75 Combine like terms: -7.04006392 + -0.75 = -7.79006392 x = -7.79006392 Simplifying x = -7.79006392Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.29006392, -7.79006392}Solution
x = {0, 6.29006392, -7.79006392}
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