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Simplifying 2x2 + 4x + -98 = 0 Reorder the terms: -98 + 4x + 2x2 = 0 Solving -98 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + 2x + x2)' equal to zero and attempt to solve: Simplifying -49 + 2x + x2 = 0 Solving -49 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 2x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 2x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 2x + x2 = 0 + 49 2x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 2x + x2 = 49 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 = 49 + 1 Reorder the terms: 1 + 2x + x2 = 49 + 1 Combine like terms: 49 + 1 = 50 1 + 2x + x2 = 50 Factor a perfect square on the left side: (x + 1)(x + 1) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 1) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 1 = 7.071067812 Simplifying x + 1 = 7.071067812 Reorder the terms: 1 + x = 7.071067812 Solving 1 + x = 7.071067812 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 = 7.071067812 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.071067812 + -1 x = 7.071067812 + -1 Combine like terms: 7.071067812 + -1 = 6.071067812 x = 6.071067812 Simplifying x = 6.071067812Subproblem 2
x + 1 = -7.071067812 Simplifying x + 1 = -7.071067812 Reorder the terms: 1 + x = -7.071067812 Solving 1 + x = -7.071067812 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 = -7.071067812 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.071067812 + -1 x = -7.071067812 + -1 Combine like terms: -7.071067812 + -1 = -8.071067812 x = -8.071067812 Simplifying x = -8.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.071067812, -8.071067812}Solution
x = {6.071067812, -8.071067812}
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