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Simplifying 4x2 + -8x + -71 = 0 Reorder the terms: -71 + -8x + 4x2 = 0 Solving -71 + -8x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.75 + -2x + x2 = 0 Move the constant term to the right: Add '17.75' to each side of the equation. -17.75 + -2x + 17.75 + x2 = 0 + 17.75 Reorder the terms: -17.75 + 17.75 + -2x + x2 = 0 + 17.75 Combine like terms: -17.75 + 17.75 = 0.00 0.00 + -2x + x2 = 0 + 17.75 -2x + x2 = 0 + 17.75 Combine like terms: 0 + 17.75 = 17.75 -2x + x2 = 17.75 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 = 17.75 + 1 Reorder the terms: 1 + -2x + x2 = 17.75 + 1 Combine like terms: 17.75 + 1 = 18.75 1 + -2x + x2 = 18.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + -1) equal to 4.330127019 and -4.330127019.Subproblem 1
x + -1 = 4.330127019 Simplifying x + -1 = 4.330127019 Reorder the terms: -1 + x = 4.330127019 Solving -1 + x = 4.330127019 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 = 4.330127019 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.330127019 + 1 x = 4.330127019 + 1 Combine like terms: 4.330127019 + 1 = 5.330127019 x = 5.330127019 Simplifying x = 5.330127019Subproblem 2
x + -1 = -4.330127019 Simplifying x + -1 = -4.330127019 Reorder the terms: -1 + x = -4.330127019 Solving -1 + x = -4.330127019 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 = -4.330127019 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.330127019 + 1 x = -4.330127019 + 1 Combine like terms: -4.330127019 + 1 = -3.330127019 x = -3.330127019 Simplifying x = -3.330127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.330127019, -3.330127019}
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