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Simplifying -2x2 + 8x + 98 = 0 Reorder the terms: 98 + 8x + -2x2 = 0 Solving 98 + 8x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(49 + 4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 49 + 4x + -1x2 = 0 Solving 49 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + -4x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + -4x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -4x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -4x + x2 = 0 + 49 -4x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -4x + x2 = 49 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 49 + 4 Reorder the terms: 4 + -4x + x2 = 49 + 4 Combine like terms: 49 + 4 = 53 4 + -4x + x2 = 53 Factor a perfect square on the left side: (x + -2)(x + -2) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + -2) equal to 7.280109889 and -7.280109889.Subproblem 1
x + -2 = 7.280109889 Simplifying x + -2 = 7.280109889 Reorder the terms: -2 + x = 7.280109889 Solving -2 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 7.280109889 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.280109889 + 2 x = 7.280109889 + 2 Combine like terms: 7.280109889 + 2 = 9.280109889 x = 9.280109889 Simplifying x = 9.280109889Subproblem 2
x + -2 = -7.280109889 Simplifying x + -2 = -7.280109889 Reorder the terms: -2 + x = -7.280109889 Solving -2 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -7.280109889 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.280109889 + 2 x = -7.280109889 + 2 Combine like terms: -7.280109889 + 2 = -5.280109889 x = -5.280109889 Simplifying x = -5.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.280109889, -5.280109889}Solution
x = {9.280109889, -5.280109889}
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