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Simplifying 2x2 + 4x = 32 Reorder the terms: 4x + 2x2 = 32 Solving 4x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 4x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + 2x + x2)' equal to zero and attempt to solve: Simplifying -16 + 2x + x2 = 0 Solving -16 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 2x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 2x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2x + x2 = 0 + 16 2x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 2x + x2 = 16 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 16 + 1 Reorder the terms: 1 + 2x + x2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + 2x + x2 = 17 Factor a perfect square on the left side: (x + 1)(x + 1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 1) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 1 = 4.123105626 Simplifying x + 1 = 4.123105626 Reorder the terms: 1 + x = 4.123105626 Solving 1 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.123105626 + -1 x = 4.123105626 + -1 Combine like terms: 4.123105626 + -1 = 3.123105626 x = 3.123105626 Simplifying x = 3.123105626Subproblem 2
x + 1 = -4.123105626 Simplifying x + 1 = -4.123105626 Reorder the terms: 1 + x = -4.123105626 Solving 1 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.123105626 + -1 x = -4.123105626 + -1 Combine like terms: -4.123105626 + -1 = -5.123105626 x = -5.123105626 Simplifying x = -5.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.123105626, -5.123105626}Solution
x = {3.123105626, -5.123105626}
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