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Simplifying 4x + 4x2 = 68 Solving 4x + 4x2 = 68 Solving for variable 'x'. Reorder the terms: -68 + 4x + 4x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + 4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-17 + x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-17 + x + x2)' equal to zero and attempt to solve: Simplifying -17 + x + x2 = 0 Solving -17 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + x + x2 = 0 + 17 x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 x + x2 = 17 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. x + 0.25 + x2 = 17 + 0.25 Reorder the terms: 0.25 + x + x2 = 17 + 0.25 Combine like terms: 17 + 0.25 = 17.25 0.25 + x + x2 = 17.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 0.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + 0.5 = 4.153311931 Simplifying x + 0.5 = 4.153311931 Reorder the terms: 0.5 + x = 4.153311931 Solving 0.5 + x = 4.153311931 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 = 4.153311931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.153311931 + -0.5 x = 4.153311931 + -0.5 Combine like terms: 4.153311931 + -0.5 = 3.653311931 x = 3.653311931 Simplifying x = 3.653311931Subproblem 2
x + 0.5 = -4.153311931 Simplifying x + 0.5 = -4.153311931 Reorder the terms: 0.5 + x = -4.153311931 Solving 0.5 + x = -4.153311931 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 = -4.153311931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.153311931 + -0.5 x = -4.153311931 + -0.5 Combine like terms: -4.153311931 + -0.5 = -4.653311931 x = -4.653311931 Simplifying x = -4.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.653311931, -4.653311931}Solution
x = {3.653311931, -4.653311931}
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