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Simplifying 0 = 8x2 + -62x + -50 Reorder the terms: 0 = -50 + -62x + 8x2 Solving 0 = -50 + -62x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 50 = 50 50 + 62x + -8x2 = -50 + -62x + 8x2 + 50 + 62x + -8x2 Reorder the terms: 50 + 62x + -8x2 = -50 + 50 + -62x + 62x + 8x2 + -8x2 Combine like terms: -50 + 50 = 0 50 + 62x + -8x2 = 0 + -62x + 62x + 8x2 + -8x2 50 + 62x + -8x2 = -62x + 62x + 8x2 + -8x2 Combine like terms: -62x + 62x = 0 50 + 62x + -8x2 = 0 + 8x2 + -8x2 50 + 62x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 50 + 62x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 31x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 31x + -4x2)' equal to zero and attempt to solve: Simplifying 25 + 31x + -4x2 = 0 Solving 25 + 31x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -7.75x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -7.75x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -7.75x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -7.75x + x2 = 0 + 6.25 -7.75x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -7.75x + x2 = 6.25 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = 6.25 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = 6.25 + 15.015625 Combine like terms: 6.25 + 15.015625 = 21.265625 15.015625 + -7.75x + x2 = 21.265625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 21.265625 Calculate the square root of the right side: 4.611466686 Break this problem into two subproblems by setting (x + -3.875) equal to 4.611466686 and -4.611466686.Subproblem 1
x + -3.875 = 4.611466686 Simplifying x + -3.875 = 4.611466686 Reorder the terms: -3.875 + x = 4.611466686 Solving -3.875 + x = 4.611466686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 4.611466686 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 4.611466686 + 3.875 x = 4.611466686 + 3.875 Combine like terms: 4.611466686 + 3.875 = 8.486466686 x = 8.486466686 Simplifying x = 8.486466686Subproblem 2
x + -3.875 = -4.611466686 Simplifying x + -3.875 = -4.611466686 Reorder the terms: -3.875 + x = -4.611466686 Solving -3.875 + x = -4.611466686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -4.611466686 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -4.611466686 + 3.875 x = -4.611466686 + 3.875 Combine like terms: -4.611466686 + 3.875 = -0.736466686 x = -0.736466686 Simplifying x = -0.736466686Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.486466686, -0.736466686}Solution
x = {8.486466686, -0.736466686}
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