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Simplifying 5x2 + -55x + -20 = 0 Reorder the terms: -20 + -55x + 5x2 = 0 Solving -20 + -55x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + -11x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + -11x + x2)' equal to zero and attempt to solve: Simplifying -4 + -11x + x2 = 0 Solving -4 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -11x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -11x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -11x + x2 = 0 + 4 -11x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -11x + x2 = 4 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 = 4 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 4 + 30.25 Combine like terms: 4 + 30.25 = 34.25 30.25 + -11x + x2 = 34.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + -5.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + -5.5 = 5.852349955 Simplifying x + -5.5 = 5.852349955 Reorder the terms: -5.5 + x = 5.852349955 Solving -5.5 + x = 5.852349955 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 = 5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.852349955 + 5.5 x = 5.852349955 + 5.5 Combine like terms: 5.852349955 + 5.5 = 11.352349955 x = 11.352349955 Simplifying x = 11.352349955Subproblem 2
x + -5.5 = -5.852349955 Simplifying x + -5.5 = -5.852349955 Reorder the terms: -5.5 + x = -5.852349955 Solving -5.5 + x = -5.852349955 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 = -5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.852349955 + 5.5 x = -5.852349955 + 5.5 Combine like terms: -5.852349955 + 5.5 = -0.352349955 x = -0.352349955 Simplifying x = -0.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.352349955, -0.352349955}Solution
x = {11.352349955, -0.352349955}
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