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Simplifying 50 = 2x(2x + -43) Reorder the terms: 50 = 2x(-43 + 2x) 50 = (-43 * 2x + 2x * 2x) 50 = (-86x + 4x2) Solving 50 = -86x + 4x2 Solving for variable 'x'. Reorder the terms: 50 + 86x + -4x2 = -86x + 86x + 4x2 + -4x2 Combine like terms: -86x + 86x = 0 50 + 86x + -4x2 = 0 + 4x2 + -4x2 50 + 86x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 50 + 86x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 43x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 43x + -2x2)' equal to zero and attempt to solve: Simplifying 25 + 43x + -2x2 = 0 Solving 25 + 43x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + -21.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -21.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -21.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -21.5x + x2 = 0 + 12.5 -21.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -21.5x + x2 = 12.5 The x term is -21.5x. Take half its coefficient (-10.75). Square it (115.5625) and add it to both sides. Add '115.5625' to each side of the equation. -21.5x + 115.5625 + x2 = 12.5 + 115.5625 Reorder the terms: 115.5625 + -21.5x + x2 = 12.5 + 115.5625 Combine like terms: 12.5 + 115.5625 = 128.0625 115.5625 + -21.5x + x2 = 128.0625 Factor a perfect square on the left side: (x + -10.75)(x + -10.75) = 128.0625 Calculate the square root of the right side: 11.316470298 Break this problem into two subproblems by setting (x + -10.75) equal to 11.316470298 and -11.316470298.Subproblem 1
x + -10.75 = 11.316470298 Simplifying x + -10.75 = 11.316470298 Reorder the terms: -10.75 + x = 11.316470298 Solving -10.75 + x = 11.316470298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.75' to each side of the equation. -10.75 + 10.75 + x = 11.316470298 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + x = 11.316470298 + 10.75 x = 11.316470298 + 10.75 Combine like terms: 11.316470298 + 10.75 = 22.066470298 x = 22.066470298 Simplifying x = 22.066470298Subproblem 2
x + -10.75 = -11.316470298 Simplifying x + -10.75 = -11.316470298 Reorder the terms: -10.75 + x = -11.316470298 Solving -10.75 + x = -11.316470298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.75' to each side of the equation. -10.75 + 10.75 + x = -11.316470298 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + x = -11.316470298 + 10.75 x = -11.316470298 + 10.75 Combine like terms: -11.316470298 + 10.75 = -0.566470298 x = -0.566470298 Simplifying x = -0.566470298Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.066470298, -0.566470298}Solution
x = {22.066470298, -0.566470298}
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