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Simplifying 3590 = 10x2 + 265x + 3100 Reorder the terms: 3590 = 3100 + 265x + 10x2 Solving 3590 = 3100 + 265x + 10x2 Solving for variable 'x'. Combine like terms: 3590 + -3100 = 490 490 + -265x + -10x2 = 3100 + 265x + 10x2 + -3100 + -265x + -10x2 Reorder the terms: 490 + -265x + -10x2 = 3100 + -3100 + 265x + -265x + 10x2 + -10x2 Combine like terms: 3100 + -3100 = 0 490 + -265x + -10x2 = 0 + 265x + -265x + 10x2 + -10x2 490 + -265x + -10x2 = 265x + -265x + 10x2 + -10x2 Combine like terms: 265x + -265x = 0 490 + -265x + -10x2 = 0 + 10x2 + -10x2 490 + -265x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 490 + -265x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(98 + -53x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(98 + -53x + -2x2)' equal to zero and attempt to solve: Simplifying 98 + -53x + -2x2 = 0 Solving 98 + -53x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -49 + 26.5x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 26.5x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 26.5x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 26.5x + x2 = 0 + 49 26.5x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 26.5x + x2 = 49 The x term is 26.5x. Take half its coefficient (13.25). Square it (175.5625) and add it to both sides. Add '175.5625' to each side of the equation. 26.5x + 175.5625 + x2 = 49 + 175.5625 Reorder the terms: 175.5625 + 26.5x + x2 = 49 + 175.5625 Combine like terms: 49 + 175.5625 = 224.5625 175.5625 + 26.5x + x2 = 224.5625 Factor a perfect square on the left side: (x + 13.25)(x + 13.25) = 224.5625 Calculate the square root of the right side: 14.985409571 Break this problem into two subproblems by setting (x + 13.25) equal to 14.985409571 and -14.985409571.Subproblem 1
x + 13.25 = 14.985409571 Simplifying x + 13.25 = 14.985409571 Reorder the terms: 13.25 + x = 14.985409571 Solving 13.25 + x = 14.985409571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.25' to each side of the equation. 13.25 + -13.25 + x = 14.985409571 + -13.25 Combine like terms: 13.25 + -13.25 = 0.00 0.00 + x = 14.985409571 + -13.25 x = 14.985409571 + -13.25 Combine like terms: 14.985409571 + -13.25 = 1.735409571 x = 1.735409571 Simplifying x = 1.735409571Subproblem 2
x + 13.25 = -14.985409571 Simplifying x + 13.25 = -14.985409571 Reorder the terms: 13.25 + x = -14.985409571 Solving 13.25 + x = -14.985409571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.25' to each side of the equation. 13.25 + -13.25 + x = -14.985409571 + -13.25 Combine like terms: 13.25 + -13.25 = 0.00 0.00 + x = -14.985409571 + -13.25 x = -14.985409571 + -13.25 Combine like terms: -14.985409571 + -13.25 = -28.235409571 x = -28.235409571 Simplifying x = -28.235409571Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.735409571, -28.235409571}Solution
x = {1.735409571, -28.235409571}
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