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Simplifying 2x2 + -16x + -14 = (2x + 1)(2x + -1) Reorder the terms: -14 + -16x + 2x2 = (2x + 1)(2x + -1) Reorder the terms: -14 + -16x + 2x2 = (1 + 2x)(2x + -1) Reorder the terms: -14 + -16x + 2x2 = (1 + 2x)(-1 + 2x) Multiply (1 + 2x) * (-1 + 2x) -14 + -16x + 2x2 = (1(-1 + 2x) + 2x * (-1 + 2x)) -14 + -16x + 2x2 = ((-1 * 1 + 2x * 1) + 2x * (-1 + 2x)) -14 + -16x + 2x2 = ((-1 + 2x) + 2x * (-1 + 2x)) -14 + -16x + 2x2 = (-1 + 2x + (-1 * 2x + 2x * 2x)) -14 + -16x + 2x2 = (-1 + 2x + (-2x + 4x2)) Combine like terms: 2x + -2x = 0 -14 + -16x + 2x2 = (-1 + 0 + 4x2) -14 + -16x + 2x2 = (-1 + 4x2) Solving -14 + -16x + 2x2 = -1 + 4x2 Solving for variable 'x'. Reorder the terms: -14 + 1 + -16x + 2x2 + -4x2 = -1 + 4x2 + 1 + -4x2 Combine like terms: -14 + 1 = -13 -13 + -16x + 2x2 + -4x2 = -1 + 4x2 + 1 + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 -13 + -16x + -2x2 = -1 + 4x2 + 1 + -4x2 Reorder the terms: -13 + -16x + -2x2 = -1 + 1 + 4x2 + -4x2 Combine like terms: -1 + 1 = 0 -13 + -16x + -2x2 = 0 + 4x2 + -4x2 -13 + -16x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -13 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 16x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 16x + 2x2)' equal to zero and attempt to solve: Simplifying 13 + 16x + 2x2 = 0 Solving 13 + 16x + 2x2 = 0 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 = 9.5 16 + 8x + x2 = 9.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + 4) equal to 3.082207001 and -3.082207001.Subproblem 1
x + 4 = 3.082207001 Simplifying x + 4 = 3.082207001 Reorder the terms: 4 + x = 3.082207001 Solving 4 + x = 3.082207001 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 = 3.082207001 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.082207001 + -4 x = 3.082207001 + -4 Combine like terms: 3.082207001 + -4 = -0.917792999 x = -0.917792999 Simplifying x = -0.917792999Subproblem 2
x + 4 = -3.082207001 Simplifying x + 4 = -3.082207001 Reorder the terms: 4 + x = -3.082207001 Solving 4 + x = -3.082207001 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 = -3.082207001 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.082207001 + -4 x = -3.082207001 + -4 Combine like terms: -3.082207001 + -4 = -7.082207001 x = -7.082207001 Simplifying x = -7.082207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.917792999, -7.082207001}Solution
x = {-0.917792999, -7.082207001}
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