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Simplifying 2x + 4x2 = 24 Solving 2x + 4x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 2x + 4x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + x + 2x2)' equal to zero and attempt to solve: Simplifying -12 + x + 2x2 = 0 Solving -12 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 0.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 0.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.5x + x2 = 0 + 6 0.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.5x + x2 = 6 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 6 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 6 + 0.25 Combine like terms: 6 + 0.25 = 6.25 0.25 + 0.5x + x2 = 6.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + 0.5) equal to 2.5 and -2.5.Subproblem 1
x + 0.5 = 2.5 Simplifying x + 0.5 = 2.5 Reorder the terms: 0.5 + x = 2.5 Solving 0.5 + x = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.5 + -0.5 x = 2.5 + -0.5 Combine like terms: 2.5 + -0.5 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 0.5 = -2.5 Simplifying x + 0.5 = -2.5 Reorder the terms: 0.5 + x = -2.5 Solving 0.5 + x = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.5 + -0.5 x = -2.5 + -0.5 Combine like terms: -2.5 + -0.5 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -3}Solution
x = {2, -3}
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