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Simplifying (25 + -2x)(20 + -2x) = 462 Multiply (25 + -2x) * (20 + -2x) (25(20 + -2x) + -2x * (20 + -2x)) = 462 ((20 * 25 + -2x * 25) + -2x * (20 + -2x)) = 462 ((500 + -50x) + -2x * (20 + -2x)) = 462 (500 + -50x + (20 * -2x + -2x * -2x)) = 462 (500 + -50x + (-40x + 4x2)) = 462 Combine like terms: -50x + -40x = -90x (500 + -90x + 4x2) = 462 Solving 500 + -90x + 4x2 = 462 Solving for variable 'x'. Reorder the terms: 500 + -462 + -90x + 4x2 = 462 + -462 Combine like terms: 500 + -462 = 38 38 + -90x + 4x2 = 462 + -462 Combine like terms: 462 + -462 = 0 38 + -90x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -45x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -45x + 2x2)' equal to zero and attempt to solve: Simplifying 19 + -45x + 2x2 = 0 Solving 19 + -45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9.5 + -22.5x + x2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + -22.5x + -9.5 + x2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + -22.5x + x2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + -22.5x + x2 = 0 + -9.5 -22.5x + x2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 -22.5x + x2 = -9.5 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = -9.5 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = -9.5 + 126.5625 Combine like terms: -9.5 + 126.5625 = 117.0625 126.5625 + -22.5x + x2 = 117.0625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 117.0625 Calculate the square root of the right side: 10.819542504 Break this problem into two subproblems by setting (x + -11.25) equal to 10.819542504 and -10.819542504.Subproblem 1
x + -11.25 = 10.819542504 Simplifying x + -11.25 = 10.819542504 Reorder the terms: -11.25 + x = 10.819542504 Solving -11.25 + x = 10.819542504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 10.819542504 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 10.819542504 + 11.25 x = 10.819542504 + 11.25 Combine like terms: 10.819542504 + 11.25 = 22.069542504 x = 22.069542504 Simplifying x = 22.069542504Subproblem 2
x + -11.25 = -10.819542504 Simplifying x + -11.25 = -10.819542504 Reorder the terms: -11.25 + x = -10.819542504 Solving -11.25 + x = -10.819542504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -10.819542504 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -10.819542504 + 11.25 x = -10.819542504 + 11.25 Combine like terms: -10.819542504 + 11.25 = 0.430457496 x = 0.430457496 Simplifying x = 0.430457496Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.069542504, 0.430457496}Solution
x = {22.069542504, 0.430457496}
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