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Simplifying (x + -2) * 45(55x) = 105 Reorder the terms: (-2 + x) * 45(55x) = 105 Remove parenthesis around (55x) (-2 + x) * 45 * 55x = 105 Reorder the terms for easier multiplication: 45 * 55x(-2 + x) = 105 Multiply 45 * 55 2475x(-2 + x) = 105 (-2 * 2475x + x * 2475x) = 105 (-4950x + 2475x2) = 105 Solving -4950x + 2475x2 = 105 Solving for variable 'x'. Reorder the terms: -105 + -4950x + 2475x2 = 105 + -105 Combine like terms: 105 + -105 = 0 -105 + -4950x + 2475x2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-7 + -330x + 165x2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-7 + -330x + 165x2)' equal to zero and attempt to solve: Simplifying -7 + -330x + 165x2 = 0 Solving -7 + -330x + 165x2 = 0 Begin completing the square. Divide all terms by 165 the coefficient of the squared term: Divide each side by '165'. -0.04242424242 + -2x + x2 = 0 Move the constant term to the right: Add '0.04242424242' to each side of the equation. -0.04242424242 + -2x + 0.04242424242 + x2 = 0 + 0.04242424242 Reorder the terms: -0.04242424242 + 0.04242424242 + -2x + x2 = 0 + 0.04242424242 Combine like terms: -0.04242424242 + 0.04242424242 = 0.00000000000 0.00000000000 + -2x + x2 = 0 + 0.04242424242 -2x + x2 = 0 + 0.04242424242 Combine like terms: 0 + 0.04242424242 = 0.04242424242 -2x + x2 = 0.04242424242 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 = 0.04242424242 + 1 Reorder the terms: 1 + -2x + x2 = 0.04242424242 + 1 Combine like terms: 0.04242424242 + 1 = 1.04242424242 1 + -2x + x2 = 1.04242424242 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.04242424242 Calculate the square root of the right side: 1.020991794 Break this problem into two subproblems by setting (x + -1) equal to 1.020991794 and -1.020991794.Subproblem 1
x + -1 = 1.020991794 Simplifying x + -1 = 1.020991794 Reorder the terms: -1 + x = 1.020991794 Solving -1 + x = 1.020991794 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 = 1.020991794 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.020991794 + 1 x = 1.020991794 + 1 Combine like terms: 1.020991794 + 1 = 2.020991794 x = 2.020991794 Simplifying x = 2.020991794Subproblem 2
x + -1 = -1.020991794 Simplifying x + -1 = -1.020991794 Reorder the terms: -1 + x = -1.020991794 Solving -1 + x = -1.020991794 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 = -1.020991794 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.020991794 + 1 x = -1.020991794 + 1 Combine like terms: -1.020991794 + 1 = -0.020991794 x = -0.020991794 Simplifying x = -0.020991794Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.020991794, -0.020991794}Solution
x = {2.020991794, -0.020991794}
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