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Simplifying 5x3 + 65x2 + 14x = 0 Reorder the terms: 14x + 65x2 + 5x3 = 0 Solving 14x + 65x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(14 + 65x + 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 '(14 + 65x + 5x2)' equal to zero and attempt to solve: Simplifying 14 + 65x + 5x2 = 0 Solving 14 + 65x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 13x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 13x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 13x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 13x + x2 = 0 + -2.8 13x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 13x + x2 = -2.8 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -2.8 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -2.8 + 42.25 Combine like terms: -2.8 + 42.25 = 39.45 42.25 + 13x + x2 = 39.45 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 39.45 Calculate the square root of the right side: 6.280923499 Break this problem into two subproblems by setting (x + 6.5) equal to 6.280923499 and -6.280923499.Subproblem 1
x + 6.5 = 6.280923499 Simplifying x + 6.5 = 6.280923499 Reorder the terms: 6.5 + x = 6.280923499 Solving 6.5 + x = 6.280923499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 6.280923499 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.280923499 + -6.5 x = 6.280923499 + -6.5 Combine like terms: 6.280923499 + -6.5 = -0.219076501 x = -0.219076501 Simplifying x = -0.219076501Subproblem 2
x + 6.5 = -6.280923499 Simplifying x + 6.5 = -6.280923499 Reorder the terms: 6.5 + x = -6.280923499 Solving 6.5 + x = -6.280923499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -6.280923499 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.280923499 + -6.5 x = -6.280923499 + -6.5 Combine like terms: -6.280923499 + -6.5 = -12.780923499 x = -12.780923499 Simplifying x = -12.780923499Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.219076501, -12.780923499}Solution
x = {0, -0.219076501, -12.780923499}
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