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Simplifying (x + 40)(x + 30) = 8x2 Reorder the terms: (40 + x)(x + 30) = 8x2 Reorder the terms: (40 + x)(30 + x) = 8x2 Multiply (40 + x) * (30 + x) (40(30 + x) + x(30 + x)) = 8x2 ((30 * 40 + x * 40) + x(30 + x)) = 8x2 ((1200 + 40x) + x(30 + x)) = 8x2 (1200 + 40x + (30 * x + x * x)) = 8x2 (1200 + 40x + (30x + x2)) = 8x2 Combine like terms: 40x + 30x = 70x (1200 + 70x + x2) = 8x2 Solving 1200 + 70x + x2 = 8x2 Solving for variable 'x'. Combine like terms: x2 + -8x2 = -7x2 1200 + 70x + -7x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 1200 + 70x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -171.4285714 + -10x + x2 = 0 Move the constant term to the right: Add '171.4285714' to each side of the equation. -171.4285714 + -10x + 171.4285714 + x2 = 0 + 171.4285714 Reorder the terms: -171.4285714 + 171.4285714 + -10x + x2 = 0 + 171.4285714 Combine like terms: -171.4285714 + 171.4285714 = 0.0000000 0.0000000 + -10x + x2 = 0 + 171.4285714 -10x + x2 = 0 + 171.4285714 Combine like terms: 0 + 171.4285714 = 171.4285714 -10x + x2 = 171.4285714 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 171.4285714 + 25 Reorder the terms: 25 + -10x + x2 = 171.4285714 + 25 Combine like terms: 171.4285714 + 25 = 196.4285714 25 + -10x + x2 = 196.4285714 Factor a perfect square on the left side: (x + -5)(x + -5) = 196.4285714 Calculate the square root of the right side: 14.015297764 Break this problem into two subproblems by setting (x + -5) equal to 14.015297764 and -14.015297764.Subproblem 1
x + -5 = 14.015297764 Simplifying x + -5 = 14.015297764 Reorder the terms: -5 + x = 14.015297764 Solving -5 + x = 14.015297764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 14.015297764 + 5 Combine like terms: -5 + 5 = 0 0 + x = 14.015297764 + 5 x = 14.015297764 + 5 Combine like terms: 14.015297764 + 5 = 19.015297764 x = 19.015297764 Simplifying x = 19.015297764Subproblem 2
x + -5 = -14.015297764 Simplifying x + -5 = -14.015297764 Reorder the terms: -5 + x = -14.015297764 Solving -5 + x = -14.015297764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -14.015297764 + 5 Combine like terms: -5 + 5 = 0 0 + x = -14.015297764 + 5 x = -14.015297764 + 5 Combine like terms: -14.015297764 + 5 = -9.015297764 x = -9.015297764 Simplifying x = -9.015297764Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.015297764, -9.015297764}
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