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Simplifying 48 = 14x + 2x2 Solving 48 = 14x + 2x2 Solving for variable 'x'. Reorder the terms: 48 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 48 + -14x + -2x2 = 0 + 2x2 + -2x2 48 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 48 + -14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 24 + -7x + -1x2 = 0 Solving 24 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 7x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 7x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 7x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 7x + x2 = 0 + 24 7x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 7x + x2 = 24 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 24 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 24 + 12.25 Combine like terms: 24 + 12.25 = 36.25 12.25 + 7x + x2 = 36.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + 3.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + 3.5 = 6.020797289 Simplifying x + 3.5 = 6.020797289 Reorder the terms: 3.5 + x = 6.020797289 Solving 3.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.020797289 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.020797289 + -3.5 x = 6.020797289 + -3.5 Combine like terms: 6.020797289 + -3.5 = 2.520797289 x = 2.520797289 Simplifying x = 2.520797289Subproblem 2
x + 3.5 = -6.020797289 Simplifying x + 3.5 = -6.020797289 Reorder the terms: 3.5 + x = -6.020797289 Solving 3.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.020797289 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.020797289 + -3.5 x = -6.020797289 + -3.5 Combine like terms: -6.020797289 + -3.5 = -9.520797289 x = -9.520797289 Simplifying x = -9.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.520797289, -9.520797289}Solution
x = {2.520797289, -9.520797289}
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