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Simplifying 2x(x + 8) = 98 Reorder the terms: 2x(8 + x) = 98 (8 * 2x + x * 2x) = 98 (16x + 2x2) = 98 Solving 16x + 2x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + 16x + 2x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + 8x + x2)' equal to zero and attempt to solve: Simplifying -49 + 8x + x2 = 0 Solving -49 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 8x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 8x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 8x + x2 = 0 + 49 8x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 8x + x2 = 49 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 49 + 16 Reorder the terms: 16 + 8x + x2 = 49 + 16 Combine like terms: 49 + 16 = 65 16 + 8x + x2 = 65 Factor a perfect square on the left side: (x + 4)(x + 4) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + 4) equal to 8.062257748 and -8.062257748.Subproblem 1
x + 4 = 8.062257748 Simplifying x + 4 = 8.062257748 Reorder the terms: 4 + x = 8.062257748 Solving 4 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 8.062257748 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.062257748 + -4 x = 8.062257748 + -4 Combine like terms: 8.062257748 + -4 = 4.062257748 x = 4.062257748 Simplifying x = 4.062257748Subproblem 2
x + 4 = -8.062257748 Simplifying x + 4 = -8.062257748 Reorder the terms: 4 + x = -8.062257748 Solving 4 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -8.062257748 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.062257748 + -4 x = -8.062257748 + -4 Combine like terms: -8.062257748 + -4 = -12.062257748 x = -12.062257748 Simplifying x = -12.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.062257748, -12.062257748}Solution
x = {4.062257748, -12.062257748}
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