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Simplifying 20x + 35x(x + 21) = 600 Reorder the terms: 20x + 35x(21 + x) = 600 20x + (21 * 35x + x * 35x) = 600 20x + (735x + 35x2) = 600 Combine like terms: 20x + 735x = 755x 755x + 35x2 = 600 Solving 755x + 35x2 = 600 Solving for variable 'x'. Reorder the terms: -600 + 755x + 35x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 755x + 35x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-120 + 151x + 7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-120 + 151x + 7x2)' equal to zero and attempt to solve: Simplifying -120 + 151x + 7x2 = 0 Solving -120 + 151x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -17.14285714 + 21.57142857x + x2 = 0 Move the constant term to the right: Add '17.14285714' to each side of the equation. -17.14285714 + 21.57142857x + 17.14285714 + x2 = 0 + 17.14285714 Reorder the terms: -17.14285714 + 17.14285714 + 21.57142857x + x2 = 0 + 17.14285714 Combine like terms: -17.14285714 + 17.14285714 = 0.00000000 0.00000000 + 21.57142857x + x2 = 0 + 17.14285714 21.57142857x + x2 = 0 + 17.14285714 Combine like terms: 0 + 17.14285714 = 17.14285714 21.57142857x + x2 = 17.14285714 The x term is 21.57142857x. Take half its coefficient (10.78571429). Square it (116.3316327) and add it to both sides. Add '116.3316327' to each side of the equation. 21.57142857x + 116.3316327 + x2 = 17.14285714 + 116.3316327 Reorder the terms: 116.3316327 + 21.57142857x + x2 = 17.14285714 + 116.3316327 Combine like terms: 17.14285714 + 116.3316327 = 133.47448984 116.3316327 + 21.57142857x + x2 = 133.47448984 Factor a perfect square on the left side: (x + 10.78571429)(x + 10.78571429) = 133.47448984 Calculate the square root of the right side: 11.553116023 Break this problem into two subproblems by setting (x + 10.78571429) equal to 11.553116023 and -11.553116023.Subproblem 1
x + 10.78571429 = 11.553116023 Simplifying x + 10.78571429 = 11.553116023 Reorder the terms: 10.78571429 + x = 11.553116023 Solving 10.78571429 + x = 11.553116023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.78571429' to each side of the equation. 10.78571429 + -10.78571429 + x = 11.553116023 + -10.78571429 Combine like terms: 10.78571429 + -10.78571429 = 0.00000000 0.00000000 + x = 11.553116023 + -10.78571429 x = 11.553116023 + -10.78571429 Combine like terms: 11.553116023 + -10.78571429 = 0.767401733 x = 0.767401733 Simplifying x = 0.767401733Subproblem 2
x + 10.78571429 = -11.553116023 Simplifying x + 10.78571429 = -11.553116023 Reorder the terms: 10.78571429 + x = -11.553116023 Solving 10.78571429 + x = -11.553116023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.78571429' to each side of the equation. 10.78571429 + -10.78571429 + x = -11.553116023 + -10.78571429 Combine like terms: 10.78571429 + -10.78571429 = 0.00000000 0.00000000 + x = -11.553116023 + -10.78571429 x = -11.553116023 + -10.78571429 Combine like terms: -11.553116023 + -10.78571429 = -22.338830313 x = -22.338830313 Simplifying x = -22.338830313Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.767401733, -22.338830313}Solution
x = {0.767401733, -22.338830313}
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