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Simplifying 40x + -2x2 = 50 Solving 40x + -2x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 40x + -2x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 40x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 20x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying -25 + 20x + -1x2 = 0 Solving -25 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -20x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -20x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -20x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -20x + x2 = 0 + -25 -20x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -20x + x2 = -25 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -25 + 100 Reorder the terms: 100 + -20x + x2 = -25 + 100 Combine like terms: -25 + 100 = 75 100 + -20x + x2 = 75 Factor a perfect square on the left side: (x + -10)(x + -10) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -10) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -10 = 8.660254038 Simplifying x + -10 = 8.660254038 Reorder the terms: -10 + x = 8.660254038 Solving -10 + x = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.660254038 + 10 x = 8.660254038 + 10 Combine like terms: 8.660254038 + 10 = 18.660254038 x = 18.660254038 Simplifying x = 18.660254038Subproblem 2
x + -10 = -8.660254038 Simplifying x + -10 = -8.660254038 Reorder the terms: -10 + x = -8.660254038 Solving -10 + x = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.660254038 + 10 x = -8.660254038 + 10 Combine like terms: -8.660254038 + 10 = 1.339745962 x = 1.339745962 Simplifying x = 1.339745962Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.660254038, 1.339745962}Solution
x = {18.660254038, 1.339745962}
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