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Simplifying 4x3 + 44x2 + 30x = 0 Reorder the terms: 30x + 44x2 + 4x3 = 0 Solving 30x + 44x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(15 + 22x + 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 '(15 + 22x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + 22x + 2x2 = 0 Solving 15 + 22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 11x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 11x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 11x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 11x + x2 = 0 + -7.5 11x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 11x + x2 = -7.5 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -7.5 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -7.5 + 30.25 Combine like terms: -7.5 + 30.25 = 22.75 30.25 + 11x + x2 = 22.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + 5.5) equal to 4.769696007 and -4.769696007.Subproblem 1
x + 5.5 = 4.769696007 Simplifying x + 5.5 = 4.769696007 Reorder the terms: 5.5 + x = 4.769696007 Solving 5.5 + x = 4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 4.769696007 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.769696007 + -5.5 x = 4.769696007 + -5.5 Combine like terms: 4.769696007 + -5.5 = -0.730303993 x = -0.730303993 Simplifying x = -0.730303993Subproblem 2
x + 5.5 = -4.769696007 Simplifying x + 5.5 = -4.769696007 Reorder the terms: 5.5 + x = -4.769696007 Solving 5.5 + x = -4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -4.769696007 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.769696007 + -5.5 x = -4.769696007 + -5.5 Combine like terms: -4.769696007 + -5.5 = -10.269696007 x = -10.269696007 Simplifying x = -10.269696007Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.730303993, -10.269696007}Solution
x = {0, -0.730303993, -10.269696007}
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