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Simplifying 4x2 + -16 = 2x + 34 Reorder the terms: -16 + 4x2 = 2x + 34 Reorder the terms: -16 + 4x2 = 34 + 2x Solving -16 + 4x2 = 34 + 2x Solving for variable 'x'. Reorder the terms: -16 + -34 + -2x + 4x2 = 34 + 2x + -34 + -2x Combine like terms: -16 + -34 = -50 -50 + -2x + 4x2 = 34 + 2x + -34 + -2x Reorder the terms: -50 + -2x + 4x2 = 34 + -34 + 2x + -2x Combine like terms: 34 + -34 = 0 -50 + -2x + 4x2 = 0 + 2x + -2x -50 + -2x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -50 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -25 + -1x + 2x2 = 0 Solving -25 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -0.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -0.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -0.5x + x2 = 0 + 12.5 -0.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -0.5x + x2 = 12.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 12.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 12.5 + 0.0625 Combine like terms: 12.5 + 0.0625 = 12.5625 0.0625 + -0.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + -0.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + -0.25 = 3.54436172 Simplifying x + -0.25 = 3.54436172 Reorder the terms: -0.25 + x = 3.54436172 Solving -0.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.54436172 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.54436172 + 0.25 x = 3.54436172 + 0.25 Combine like terms: 3.54436172 + 0.25 = 3.79436172 x = 3.79436172 Simplifying x = 3.79436172Subproblem 2
x + -0.25 = -3.54436172 Simplifying x + -0.25 = -3.54436172 Reorder the terms: -0.25 + x = -3.54436172 Solving -0.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.54436172 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.54436172 + 0.25 x = -3.54436172 + 0.25 Combine like terms: -3.54436172 + 0.25 = -3.29436172 x = -3.29436172 Simplifying x = -3.29436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.79436172, -3.29436172}Solution
x = {3.79436172, -3.29436172}
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