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Simplifying x2 + 16 = 2x2 + 14x + 24 Reorder the terms: 16 + x2 = 2x2 + 14x + 24 Reorder the terms: 16 + x2 = 24 + 14x + 2x2 Solving 16 + x2 = 24 + 14x + 2x2 Solving for variable 'x'. Reorder the terms: 16 + -24 + -14x + x2 + -2x2 = 24 + 14x + 2x2 + -24 + -14x + -2x2 Combine like terms: 16 + -24 = -8 -8 + -14x + x2 + -2x2 = 24 + 14x + 2x2 + -24 + -14x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -8 + -14x + -1x2 = 24 + 14x + 2x2 + -24 + -14x + -2x2 Reorder the terms: -8 + -14x + -1x2 = 24 + -24 + 14x + -14x + 2x2 + -2x2 Combine like terms: 24 + -24 = 0 -8 + -14x + -1x2 = 0 + 14x + -14x + 2x2 + -2x2 -8 + -14x + -1x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 -8 + -14x + -1x2 = 0 + 2x2 + -2x2 -8 + -14x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + -14x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 14x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 14x + x2)' equal to zero and attempt to solve: Simplifying 8 + 14x + x2 = 0 Solving 8 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 14x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 14x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 14x + x2 = 0 + -8 14x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 14x + x2 = -8 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 = -8 + 49 Reorder the terms: 49 + 14x + x2 = -8 + 49 Combine like terms: -8 + 49 = 41 49 + 14x + x2 = 41 Factor a perfect square on the left side: (x + 7)(x + 7) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 7) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 7 = 6.403124237 Simplifying x + 7 = 6.403124237 Reorder the terms: 7 + x = 6.403124237 Solving 7 + x = 6.403124237 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 = 6.403124237 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.403124237 + -7 x = 6.403124237 + -7 Combine like terms: 6.403124237 + -7 = -0.596875763 x = -0.596875763 Simplifying x = -0.596875763Subproblem 2
x + 7 = -6.403124237 Simplifying x + 7 = -6.403124237 Reorder the terms: 7 + x = -6.403124237 Solving 7 + x = -6.403124237 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 = -6.403124237 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.403124237 + -7 x = -6.403124237 + -7 Combine like terms: -6.403124237 + -7 = -13.403124237 x = -13.403124237 Simplifying x = -13.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.596875763, -13.403124237}Solution
x = {-0.596875763, -13.403124237}
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