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Simplifying 2x2 + 12x + 16 = 4x2 + -16x + -16 Reorder the terms: 16 + 12x + 2x2 = 4x2 + -16x + -16 Reorder the terms: 16 + 12x + 2x2 = -16 + -16x + 4x2 Solving 16 + 12x + 2x2 = -16 + -16x + 4x2 Solving for variable 'x'. Reorder the terms: 16 + 16 + 12x + 16x + 2x2 + -4x2 = -16 + -16x + 4x2 + 16 + 16x + -4x2 Combine like terms: 16 + 16 = 32 32 + 12x + 16x + 2x2 + -4x2 = -16 + -16x + 4x2 + 16 + 16x + -4x2 Combine like terms: 12x + 16x = 28x 32 + 28x + 2x2 + -4x2 = -16 + -16x + 4x2 + 16 + 16x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 32 + 28x + -2x2 = -16 + -16x + 4x2 + 16 + 16x + -4x2 Reorder the terms: 32 + 28x + -2x2 = -16 + 16 + -16x + 16x + 4x2 + -4x2 Combine like terms: -16 + 16 = 0 32 + 28x + -2x2 = 0 + -16x + 16x + 4x2 + -4x2 32 + 28x + -2x2 = -16x + 16x + 4x2 + -4x2 Combine like terms: -16x + 16x = 0 32 + 28x + -2x2 = 0 + 4x2 + -4x2 32 + 28x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 32 + 28x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 14x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + 14x + -1x2)' equal to zero and attempt to solve: Simplifying 16 + 14x + -1x2 = 0 Solving 16 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + -14x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -14x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -14x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -14x + x2 = 0 + 16 -14x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -14x + x2 = 16 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 16 + 49 Reorder the terms: 49 + -14x + x2 = 16 + 49 Combine like terms: 16 + 49 = 65 49 + -14x + x2 = 65 Factor a perfect square on the left side: (x + -7)(x + -7) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -7) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -7 = 8.062257748 Simplifying x + -7 = 8.062257748 Reorder the terms: -7 + x = 8.062257748 Solving -7 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 8.062257748 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.062257748 + 7 x = 8.062257748 + 7 Combine like terms: 8.062257748 + 7 = 15.062257748 x = 15.062257748 Simplifying x = 15.062257748Subproblem 2
x + -7 = -8.062257748 Simplifying x + -7 = -8.062257748 Reorder the terms: -7 + x = -8.062257748 Solving -7 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -8.062257748 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.062257748 + 7 x = -8.062257748 + 7 Combine like terms: -8.062257748 + 7 = -1.062257748 x = -1.062257748 Simplifying x = -1.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.062257748, -1.062257748}Solution
x = {15.062257748, -1.062257748}
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