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Simplifying 2x2 + -16x + -13 = 0 Reorder the terms: -13 + -16x + 2x2 = 0 Solving -13 + -16x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + -8x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -8x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -8x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -8x + x2 = 0 + 6.5 -8x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -8x + x2 = 6.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 6.5 + 16 Reorder the terms: 16 + -8x + x2 = 6.5 + 16 Combine like terms: 6.5 + 16 = 22.5 16 + -8x + x2 = 22.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + -4) equal to 4.74341649 and -4.74341649.Subproblem 1
x + -4 = 4.74341649 Simplifying x + -4 = 4.74341649 Reorder the terms: -4 + x = 4.74341649 Solving -4 + x = 4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.74341649 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.74341649 + 4 x = 4.74341649 + 4 Combine like terms: 4.74341649 + 4 = 8.74341649 x = 8.74341649 Simplifying x = 8.74341649Subproblem 2
x + -4 = -4.74341649 Simplifying x + -4 = -4.74341649 Reorder the terms: -4 + x = -4.74341649 Solving -4 + x = -4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.74341649 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.74341649 + 4 x = -4.74341649 + 4 Combine like terms: -4.74341649 + 4 = -0.74341649 x = -0.74341649 Simplifying x = -0.74341649Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.74341649, -0.74341649}
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