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Simplifying (-10) * x2 + 685x + 22315 = 0 Reorder the terms: 22315 + 685x + -10x2 = 0 Solving 22315 + 685x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(4463 + 137x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4463 + 137x + -2x2)' equal to zero and attempt to solve: Simplifying 4463 + 137x + -2x2 = 0 Solving 4463 + 137x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2231.5 + -68.5x + x2 = 0 Move the constant term to the right: Add '2231.5' to each side of the equation. -2231.5 + -68.5x + 2231.5 + x2 = 0 + 2231.5 Reorder the terms: -2231.5 + 2231.5 + -68.5x + x2 = 0 + 2231.5 Combine like terms: -2231.5 + 2231.5 = 0.0 0.0 + -68.5x + x2 = 0 + 2231.5 -68.5x + x2 = 0 + 2231.5 Combine like terms: 0 + 2231.5 = 2231.5 -68.5x + x2 = 2231.5 The x term is -68.5x. Take half its coefficient (-34.25). Square it (1173.0625) and add it to both sides. Add '1173.0625' to each side of the equation. -68.5x + 1173.0625 + x2 = 2231.5 + 1173.0625 Reorder the terms: 1173.0625 + -68.5x + x2 = 2231.5 + 1173.0625 Combine like terms: 2231.5 + 1173.0625 = 3404.5625 1173.0625 + -68.5x + x2 = 3404.5625 Factor a perfect square on the left side: (x + -34.25)(x + -34.25) = 3404.5625 Calculate the square root of the right side: 58.348628947 Break this problem into two subproblems by setting (x + -34.25) equal to 58.348628947 and -58.348628947.Subproblem 1
x + -34.25 = 58.348628947 Simplifying x + -34.25 = 58.348628947 Reorder the terms: -34.25 + x = 58.348628947 Solving -34.25 + x = 58.348628947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34.25' to each side of the equation. -34.25 + 34.25 + x = 58.348628947 + 34.25 Combine like terms: -34.25 + 34.25 = 0.00 0.00 + x = 58.348628947 + 34.25 x = 58.348628947 + 34.25 Combine like terms: 58.348628947 + 34.25 = 92.598628947 x = 92.598628947 Simplifying x = 92.598628947Subproblem 2
x + -34.25 = -58.348628947 Simplifying x + -34.25 = -58.348628947 Reorder the terms: -34.25 + x = -58.348628947 Solving -34.25 + x = -58.348628947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34.25' to each side of the equation. -34.25 + 34.25 + x = -58.348628947 + 34.25 Combine like terms: -34.25 + 34.25 = 0.00 0.00 + x = -58.348628947 + 34.25 x = -58.348628947 + 34.25 Combine like terms: -58.348628947 + 34.25 = -24.098628947 x = -24.098628947 Simplifying x = -24.098628947Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.598628947, -24.098628947}Solution
x = {92.598628947, -24.098628947}
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