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Simplifying 88646.4 = (48 + 2x)(2x) Remove parenthesis around (2x) 88646.4 = (48 + 2x) * 2x Reorder the terms for easier multiplication: 88646.4 = 2x(48 + 2x) 88646.4 = (48 * 2x + 2x * 2x) 88646.4 = (96x + 4x2) Solving 88646.4 = 96x + 4x2 Solving for variable 'x'. Reorder the terms: 88646.4 + -96x + -4x2 = 96x + -96x + 4x2 + -4x2 Combine like terms: 96x + -96x = 0 88646.4 + -96x + -4x2 = 0 + 4x2 + -4x2 88646.4 + -96x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 88646.4 + -96x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -22161.6 + 24x + x2 = 0 Move the constant term to the right: Add '22161.6' to each side of the equation. -22161.6 + 24x + 22161.6 + x2 = 0 + 22161.6 Reorder the terms: -22161.6 + 22161.6 + 24x + x2 = 0 + 22161.6 Combine like terms: -22161.6 + 22161.6 = 0.0 0.0 + 24x + x2 = 0 + 22161.6 24x + x2 = 0 + 22161.6 Combine like terms: 0 + 22161.6 = 22161.6 24x + x2 = 22161.6 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 22161.6 + 144 Reorder the terms: 144 + 24x + x2 = 22161.6 + 144 Combine like terms: 22161.6 + 144 = 22305.6 144 + 24x + x2 = 22305.6 Factor a perfect square on the left side: (x + 12)(x + 12) = 22305.6 Calculate the square root of the right side: 149.350594241 Break this problem into two subproblems by setting (x + 12) equal to 149.350594241 and -149.350594241.Subproblem 1
x + 12 = 149.350594241 Simplifying x + 12 = 149.350594241 Reorder the terms: 12 + x = 149.350594241 Solving 12 + x = 149.350594241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 149.350594241 + -12 Combine like terms: 12 + -12 = 0 0 + x = 149.350594241 + -12 x = 149.350594241 + -12 Combine like terms: 149.350594241 + -12 = 137.350594241 x = 137.350594241 Simplifying x = 137.350594241Subproblem 2
x + 12 = -149.350594241 Simplifying x + 12 = -149.350594241 Reorder the terms: 12 + x = -149.350594241 Solving 12 + x = -149.350594241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -149.350594241 + -12 Combine like terms: 12 + -12 = 0 0 + x = -149.350594241 + -12 x = -149.350594241 + -12 Combine like terms: -149.350594241 + -12 = -161.350594241 x = -161.350594241 Simplifying x = -161.350594241Solution
The solution to the problem is based on the solutions from the subproblems. x = {137.350594241, -161.350594241}
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