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Simplifying 5x3 + 22x2 + -16x = 0 Reorder the terms: -16x + 22x2 + 5x3 = 0 Solving -16x + 22x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-16 + 22x + 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 '(-16 + 22x + 5x2)' equal to zero and attempt to solve: Simplifying -16 + 22x + 5x2 = 0 Solving -16 + 22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + 4.4x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 4.4x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 4.4x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 4.4x + x2 = 0 + 3.2 4.4x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 4.4x + x2 = 3.2 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = 3.2 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = 3.2 + 4.84 Combine like terms: 3.2 + 4.84 = 8.04 4.84 + 4.4x + x2 = 8.04 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 8.04 Calculate the square root of the right side: 2.835489376 Break this problem into two subproblems by setting (x + 2.2) equal to 2.835489376 and -2.835489376.Subproblem 1
x + 2.2 = 2.835489376 Simplifying x + 2.2 = 2.835489376 Reorder the terms: 2.2 + x = 2.835489376 Solving 2.2 + x = 2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 2.835489376 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 2.835489376 + -2.2 x = 2.835489376 + -2.2 Combine like terms: 2.835489376 + -2.2 = 0.635489376 x = 0.635489376 Simplifying x = 0.635489376Subproblem 2
x + 2.2 = -2.835489376 Simplifying x + 2.2 = -2.835489376 Reorder the terms: 2.2 + x = -2.835489376 Solving 2.2 + x = -2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -2.835489376 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -2.835489376 + -2.2 x = -2.835489376 + -2.2 Combine like terms: -2.835489376 + -2.2 = -5.035489376 x = -5.035489376 Simplifying x = -5.035489376Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.635489376, -5.035489376}Solution
x = {0, 0.635489376, -5.035489376}
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