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Simplifying 5600 = 10x2 + 305x + 3800 Reorder the terms: 5600 = 3800 + 305x + 10x2 Solving 5600 = 3800 + 305x + 10x2 Solving for variable 'x'. Combine like terms: 5600 + -3800 = 1800 1800 + -305x + -10x2 = 3800 + 305x + 10x2 + -3800 + -305x + -10x2 Reorder the terms: 1800 + -305x + -10x2 = 3800 + -3800 + 305x + -305x + 10x2 + -10x2 Combine like terms: 3800 + -3800 = 0 1800 + -305x + -10x2 = 0 + 305x + -305x + 10x2 + -10x2 1800 + -305x + -10x2 = 305x + -305x + 10x2 + -10x2 Combine like terms: 305x + -305x = 0 1800 + -305x + -10x2 = 0 + 10x2 + -10x2 1800 + -305x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 1800 + -305x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(360 + -61x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(360 + -61x + -2x2)' equal to zero and attempt to solve: Simplifying 360 + -61x + -2x2 = 0 Solving 360 + -61x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -180 + 30.5x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 30.5x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 30.5x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 30.5x + x2 = 0 + 180 30.5x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 30.5x + x2 = 180 The x term is 30.5x. Take half its coefficient (15.25). Square it (232.5625) and add it to both sides. Add '232.5625' to each side of the equation. 30.5x + 232.5625 + x2 = 180 + 232.5625 Reorder the terms: 232.5625 + 30.5x + x2 = 180 + 232.5625 Combine like terms: 180 + 232.5625 = 412.5625 232.5625 + 30.5x + x2 = 412.5625 Factor a perfect square on the left side: (x + 15.25)(x + 15.25) = 412.5625 Calculate the square root of the right side: 20.311634597 Break this problem into two subproblems by setting (x + 15.25) equal to 20.311634597 and -20.311634597.Subproblem 1
x + 15.25 = 20.311634597 Simplifying x + 15.25 = 20.311634597 Reorder the terms: 15.25 + x = 20.311634597 Solving 15.25 + x = 20.311634597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.25' to each side of the equation. 15.25 + -15.25 + x = 20.311634597 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + x = 20.311634597 + -15.25 x = 20.311634597 + -15.25 Combine like terms: 20.311634597 + -15.25 = 5.061634597 x = 5.061634597 Simplifying x = 5.061634597Subproblem 2
x + 15.25 = -20.311634597 Simplifying x + 15.25 = -20.311634597 Reorder the terms: 15.25 + x = -20.311634597 Solving 15.25 + x = -20.311634597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.25' to each side of the equation. 15.25 + -15.25 + x = -20.311634597 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + x = -20.311634597 + -15.25 x = -20.311634597 + -15.25 Combine like terms: -20.311634597 + -15.25 = -35.561634597 x = -35.561634597 Simplifying x = -35.561634597Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.061634597, -35.561634597}Solution
x = {5.061634597, -35.561634597}
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