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Simplifying x2 + x2 + 14x + 49 = 4x2 + 2x + 1 Reorder the terms: 49 + 14x + x2 + x2 = 4x2 + 2x + 1 Combine like terms: x2 + x2 = 2x2 49 + 14x + 2x2 = 4x2 + 2x + 1 Reorder the terms: 49 + 14x + 2x2 = 1 + 2x + 4x2 Solving 49 + 14x + 2x2 = 1 + 2x + 4x2 Solving for variable 'x'. Reorder the terms: 49 + -1 + 14x + -2x + 2x2 + -4x2 = 1 + 2x + 4x2 + -1 + -2x + -4x2 Combine like terms: 49 + -1 = 48 48 + 14x + -2x + 2x2 + -4x2 = 1 + 2x + 4x2 + -1 + -2x + -4x2 Combine like terms: 14x + -2x = 12x 48 + 12x + 2x2 + -4x2 = 1 + 2x + 4x2 + -1 + -2x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 48 + 12x + -2x2 = 1 + 2x + 4x2 + -1 + -2x + -4x2 Reorder the terms: 48 + 12x + -2x2 = 1 + -1 + 2x + -2x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 48 + 12x + -2x2 = 0 + 2x + -2x + 4x2 + -4x2 48 + 12x + -2x2 = 2x + -2x + 4x2 + -4x2 Combine like terms: 2x + -2x = 0 48 + 12x + -2x2 = 0 + 4x2 + -4x2 48 + 12x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 48 + 12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 24 + 6x + -1x2 = 0 Solving 24 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + -6x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -6x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -6x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -6x + x2 = 0 + 24 -6x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -6x + x2 = 24 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 24 + 9 Reorder the terms: 9 + -6x + x2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + -6x + x2 = 33 Factor a perfect square on the left side: (x + -3)(x + -3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + -3) equal to 5.744562647 and -5.744562647.Subproblem 1
x + -3 = 5.744562647 Simplifying x + -3 = 5.744562647 Reorder the terms: -3 + x = 5.744562647 Solving -3 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.744562647 + 3 x = 5.744562647 + 3 Combine like terms: 5.744562647 + 3 = 8.744562647 x = 8.744562647 Simplifying x = 8.744562647Subproblem 2
x + -3 = -5.744562647 Simplifying x + -3 = -5.744562647 Reorder the terms: -3 + x = -5.744562647 Solving -3 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.744562647 + 3 x = -5.744562647 + 3 Combine like terms: -5.744562647 + 3 = -2.744562647 x = -2.744562647 Simplifying x = -2.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.744562647, -2.744562647}Solution
x = {8.744562647, -2.744562647}
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