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Simplifying 100x2 = 230x + 132 Reorder the terms: 100x2 = 132 + 230x Solving 100x2 = 132 + 230x Solving for variable 'x'. Reorder the terms: -132 + -230x + 100x2 = 132 + 230x + -132 + -230x Reorder the terms: -132 + -230x + 100x2 = 132 + -132 + 230x + -230x Combine like terms: 132 + -132 = 0 -132 + -230x + 100x2 = 0 + 230x + -230x -132 + -230x + 100x2 = 230x + -230x Combine like terms: 230x + -230x = 0 -132 + -230x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-66 + -115x + 50x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-66 + -115x + 50x2)' equal to zero and attempt to solve: Simplifying -66 + -115x + 50x2 = 0 Solving -66 + -115x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -1.32 + -2.3x + x2 = 0.0 Move the constant term to the right: Add '1.32' to each side of the equation. -1.32 + -2.3x + 1.32 + x2 = 0.0 + 1.32 Reorder the terms: -1.32 + 1.32 + -2.3x + x2 = 0.0 + 1.32 Combine like terms: -1.32 + 1.32 = 0.00 0.00 + -2.3x + x2 = 0.0 + 1.32 -2.3x + x2 = 0.0 + 1.32 Combine like terms: 0.0 + 1.32 = 1.32 -2.3x + x2 = 1.32 The x term is -2.3x. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3x + 1.3225 + x2 = 1.32 + 1.3225 Reorder the terms: 1.3225 + -2.3x + x2 = 1.32 + 1.3225 Combine like terms: 1.32 + 1.3225 = 2.6425 1.3225 + -2.3x + x2 = 2.6425 Factor a perfect square on the left side: (x + -1.15)(x + -1.15) = 2.6425 Calculate the square root of the right side: 1.625576821 Break this problem into two subproblems by setting (x + -1.15) equal to 1.625576821 and -1.625576821.Subproblem 1
x + -1.15 = 1.625576821 Simplifying x + -1.15 = 1.625576821 Reorder the terms: -1.15 + x = 1.625576821 Solving -1.15 + x = 1.625576821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = 1.625576821 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = 1.625576821 + 1.15 x = 1.625576821 + 1.15 Combine like terms: 1.625576821 + 1.15 = 2.775576821 x = 2.775576821 Simplifying x = 2.775576821Subproblem 2
x + -1.15 = -1.625576821 Simplifying x + -1.15 = -1.625576821 Reorder the terms: -1.15 + x = -1.625576821 Solving -1.15 + x = -1.625576821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = -1.625576821 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = -1.625576821 + 1.15 x = -1.625576821 + 1.15 Combine like terms: -1.625576821 + 1.15 = -0.475576821 x = -0.475576821 Simplifying x = -0.475576821Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.775576821, -0.475576821}Solution
x = {2.775576821, -0.475576821}
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