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Simplifying 100x2 + 55x + 3 = 50x2 + -55x + 23 Reorder the terms: 3 + 55x + 100x2 = 50x2 + -55x + 23 Reorder the terms: 3 + 55x + 100x2 = 23 + -55x + 50x2 Solving 3 + 55x + 100x2 = 23 + -55x + 50x2 Solving for variable 'x'. Reorder the terms: 3 + -23 + 55x + 55x + 100x2 + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Combine like terms: 3 + -23 = -20 -20 + 55x + 55x + 100x2 + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Combine like terms: 55x + 55x = 110x -20 + 110x + 100x2 + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Combine like terms: 100x2 + -50x2 = 50x2 -20 + 110x + 50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Reorder the terms: -20 + 110x + 50x2 = 23 + -23 + -55x + 55x + 50x2 + -50x2 Combine like terms: 23 + -23 = 0 -20 + 110x + 50x2 = 0 + -55x + 55x + 50x2 + -50x2 -20 + 110x + 50x2 = -55x + 55x + 50x2 + -50x2 Combine like terms: -55x + 55x = 0 -20 + 110x + 50x2 = 0 + 50x2 + -50x2 -20 + 110x + 50x2 = 50x2 + -50x2 Combine like terms: 50x2 + -50x2 = 0 -20 + 110x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-2 + 11x + 5x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-2 + 11x + 5x2)' equal to zero and attempt to solve: Simplifying -2 + 11x + 5x2 = 0 Solving -2 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 2.2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2.2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2.2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2.2x + x2 = 0 + 0.4 2.2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2.2x + x2 = 0.4 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 0.4 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 0.4 + 1.21 Combine like terms: 0.4 + 1.21 = 1.61 1.21 + 2.2x + x2 = 1.61 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x + 1.1) equal to 1.268857754 and -1.268857754.Subproblem 1
x + 1.1 = 1.268857754 Simplifying x + 1.1 = 1.268857754 Reorder the terms: 1.1 + x = 1.268857754 Solving 1.1 + x = 1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.268857754 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.268857754 + -1.1 x = 1.268857754 + -1.1 Combine like terms: 1.268857754 + -1.1 = 0.168857754 x = 0.168857754 Simplifying x = 0.168857754Subproblem 2
x + 1.1 = -1.268857754 Simplifying x + 1.1 = -1.268857754 Reorder the terms: 1.1 + x = -1.268857754 Solving 1.1 + x = -1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.268857754 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.268857754 + -1.1 x = -1.268857754 + -1.1 Combine like terms: -1.268857754 + -1.1 = -2.368857754 x = -2.368857754 Simplifying x = -2.368857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.168857754, -2.368857754}Solution
x = {0.168857754, -2.368857754}
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