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Simplifying 4x2 + -8x + -86 = 0 Reorder the terms: -86 + -8x + 4x2 = 0 Solving -86 + -8x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-43 + -4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-43 + -4x + 2x2)' equal to zero and attempt to solve: Simplifying -43 + -4x + 2x2 = 0 Solving -43 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21.5 + -2x + x2 = 0 Move the constant term to the right: Add '21.5' to each side of the equation. -21.5 + -2x + 21.5 + x2 = 0 + 21.5 Reorder the terms: -21.5 + 21.5 + -2x + x2 = 0 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + -2x + x2 = 0 + 21.5 -2x + x2 = 0 + 21.5 Combine like terms: 0 + 21.5 = 21.5 -2x + x2 = 21.5 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 = 21.5 + 1 Reorder the terms: 1 + -2x + x2 = 21.5 + 1 Combine like terms: 21.5 + 1 = 22.5 1 + -2x + x2 = 22.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + -1) equal to 4.74341649 and -4.74341649.Subproblem 1
x + -1 = 4.74341649 Simplifying x + -1 = 4.74341649 Reorder the terms: -1 + x = 4.74341649 Solving -1 + x = 4.74341649 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 = 4.74341649 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.74341649 + 1 x = 4.74341649 + 1 Combine like terms: 4.74341649 + 1 = 5.74341649 x = 5.74341649 Simplifying x = 5.74341649Subproblem 2
x + -1 = -4.74341649 Simplifying x + -1 = -4.74341649 Reorder the terms: -1 + x = -4.74341649 Solving -1 + x = -4.74341649 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 = -4.74341649 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.74341649 + 1 x = -4.74341649 + 1 Combine like terms: -4.74341649 + 1 = -3.74341649 x = -3.74341649 Simplifying x = -3.74341649Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.74341649, -3.74341649}Solution
x = {5.74341649, -3.74341649}
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