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Simplifying 50x2 + -100x + -110 = 0 Reorder the terms: -110 + -100x + 50x2 = 0 Solving -110 + -100x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-11 + -10x + 5x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-11 + -10x + 5x2)' equal to zero and attempt to solve: Simplifying -11 + -10x + 5x2 = 0 Solving -11 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + -2x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -2x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -2x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -2x + x2 = 0 + 2.2 -2x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -2x + x2 = 2.2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 2.2 + 1 Reorder the terms: 1 + -2x + x2 = 2.2 + 1 Combine like terms: 2.2 + 1 = 3.2 1 + -2x + x2 = 3.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.2 Calculate the square root of the right side: 1.788854382 Break this problem into two subproblems by setting (x + -1) equal to 1.788854382 and -1.788854382.Subproblem 1
x + -1 = 1.788854382 Simplifying x + -1 = 1.788854382 Reorder the terms: -1 + x = 1.788854382 Solving -1 + x = 1.788854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.788854382 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.788854382 + 1 x = 1.788854382 + 1 Combine like terms: 1.788854382 + 1 = 2.788854382 x = 2.788854382 Simplifying x = 2.788854382Subproblem 2
x + -1 = -1.788854382 Simplifying x + -1 = -1.788854382 Reorder the terms: -1 + x = -1.788854382 Solving -1 + x = -1.788854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.788854382 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.788854382 + 1 x = -1.788854382 + 1 Combine like terms: -1.788854382 + 1 = -0.788854382 x = -0.788854382 Simplifying x = -0.788854382Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.788854382, -0.788854382}Solution
x = {2.788854382, -0.788854382}
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