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Simplifying 14x2 + 98x = 10x2 + 88 Reorder the terms: 98x + 14x2 = 10x2 + 88 Reorder the terms: 98x + 14x2 = 88 + 10x2 Solving 98x + 14x2 = 88 + 10x2 Solving for variable 'x'. Reorder the terms: -88 + 98x + 14x2 + -10x2 = 88 + 10x2 + -88 + -10x2 Combine like terms: 14x2 + -10x2 = 4x2 -88 + 98x + 4x2 = 88 + 10x2 + -88 + -10x2 Reorder the terms: -88 + 98x + 4x2 = 88 + -88 + 10x2 + -10x2 Combine like terms: 88 + -88 = 0 -88 + 98x + 4x2 = 0 + 10x2 + -10x2 -88 + 98x + 4x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -88 + 98x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-44 + 49x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-44 + 49x + 2x2)' equal to zero and attempt to solve: Simplifying -44 + 49x + 2x2 = 0 Solving -44 + 49x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22 + 24.5x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 24.5x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 24.5x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 24.5x + x2 = 0 + 22 24.5x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 24.5x + x2 = 22 The x term is 24.5x. Take half its coefficient (12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. 24.5x + 150.0625 + x2 = 22 + 150.0625 Reorder the terms: 150.0625 + 24.5x + x2 = 22 + 150.0625 Combine like terms: 22 + 150.0625 = 172.0625 150.0625 + 24.5x + x2 = 172.0625 Factor a perfect square on the left side: (x + 12.25)(x + 12.25) = 172.0625 Calculate the square root of the right side: 13.117259622 Break this problem into two subproblems by setting (x + 12.25) equal to 13.117259622 and -13.117259622.Subproblem 1
x + 12.25 = 13.117259622 Simplifying x + 12.25 = 13.117259622 Reorder the terms: 12.25 + x = 13.117259622 Solving 12.25 + x = 13.117259622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25' to each side of the equation. 12.25 + -12.25 + x = 13.117259622 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + x = 13.117259622 + -12.25 x = 13.117259622 + -12.25 Combine like terms: 13.117259622 + -12.25 = 0.867259622 x = 0.867259622 Simplifying x = 0.867259622Subproblem 2
x + 12.25 = -13.117259622 Simplifying x + 12.25 = -13.117259622 Reorder the terms: 12.25 + x = -13.117259622 Solving 12.25 + x = -13.117259622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25' to each side of the equation. 12.25 + -12.25 + x = -13.117259622 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + x = -13.117259622 + -12.25 x = -13.117259622 + -12.25 Combine like terms: -13.117259622 + -12.25 = -25.367259622 x = -25.367259622 Simplifying x = -25.367259622Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.867259622, -25.367259622}Solution
x = {0.867259622, -25.367259622}
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