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Simplifying 2x(4x + 10) = 180 Reorder the terms: 2x(10 + 4x) = 180 (10 * 2x + 4x * 2x) = 180 (20x + 8x2) = 180 Solving 20x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 20x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 20x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 5x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -45 + 5x + 2x2 = 0 Solving -45 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 2.5x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 2.5x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 2.5x + x2 = 0 + 22.5 2.5x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 2.5x + x2 = 22.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 22.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 22.5 + 1.5625 Combine like terms: 22.5 + 1.5625 = 24.0625 1.5625 + 2.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + 1.25) equal to 4.905354218 and -4.905354218.Subproblem 1
x + 1.25 = 4.905354218 Simplifying x + 1.25 = 4.905354218 Reorder the terms: 1.25 + x = 4.905354218 Solving 1.25 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 4.905354218 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 4.905354218 + -1.25 x = 4.905354218 + -1.25 Combine like terms: 4.905354218 + -1.25 = 3.655354218 x = 3.655354218 Simplifying x = 3.655354218Subproblem 2
x + 1.25 = -4.905354218 Simplifying x + 1.25 = -4.905354218 Reorder the terms: 1.25 + x = -4.905354218 Solving 1.25 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -4.905354218 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -4.905354218 + -1.25 x = -4.905354218 + -1.25 Combine like terms: -4.905354218 + -1.25 = -6.155354218 x = -6.155354218 Simplifying x = -6.155354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.655354218, -6.155354218}Solution
x = {3.655354218, -6.155354218}
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