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Simplifying 2x(x + 8) = 90 Reorder the terms: 2x(8 + x) = 90 (8 * 2x + x * 2x) = 90 (16x + 2x2) = 90 Solving 16x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 16x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + 8x + x2)' equal to zero and attempt to solve: Simplifying -45 + 8x + x2 = 0 Solving -45 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 8x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 8x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 8x + x2 = 0 + 45 8x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 8x + x2 = 45 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 = 45 + 16 Reorder the terms: 16 + 8x + x2 = 45 + 16 Combine like terms: 45 + 16 = 61 16 + 8x + x2 = 61 Factor a perfect square on the left side: (x + 4)(x + 4) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + 4) equal to 7.810249676 and -7.810249676.Subproblem 1
x + 4 = 7.810249676 Simplifying x + 4 = 7.810249676 Reorder the terms: 4 + x = 7.810249676 Solving 4 + x = 7.810249676 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 = 7.810249676 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.810249676 + -4 x = 7.810249676 + -4 Combine like terms: 7.810249676 + -4 = 3.810249676 x = 3.810249676 Simplifying x = 3.810249676Subproblem 2
x + 4 = -7.810249676 Simplifying x + 4 = -7.810249676 Reorder the terms: 4 + x = -7.810249676 Solving 4 + x = -7.810249676 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 = -7.810249676 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.810249676 + -4 x = -7.810249676 + -4 Combine like terms: -7.810249676 + -4 = -11.810249676 x = -11.810249676 Simplifying x = -11.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.810249676, -11.810249676}Solution
x = {3.810249676, -11.810249676}
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