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Simplifying -25x2 + 11700 + 260x = 0 Reorder the terms: 11700 + 260x + -25x2 = 0 Solving 11700 + 260x + -25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(2340 + 52x + -5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2340 + 52x + -5x2)' equal to zero and attempt to solve: Simplifying 2340 + 52x + -5x2 = 0 Solving 2340 + 52x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -468 + -10.4x + x2 = 0 Move the constant term to the right: Add '468' to each side of the equation. -468 + -10.4x + 468 + x2 = 0 + 468 Reorder the terms: -468 + 468 + -10.4x + x2 = 0 + 468 Combine like terms: -468 + 468 = 0 0 + -10.4x + x2 = 0 + 468 -10.4x + x2 = 0 + 468 Combine like terms: 0 + 468 = 468 -10.4x + x2 = 468 The x term is -10.4x. Take half its coefficient (-5.2). Square it (27.04) and add it to both sides. Add '27.04' to each side of the equation. -10.4x + 27.04 + x2 = 468 + 27.04 Reorder the terms: 27.04 + -10.4x + x2 = 468 + 27.04 Combine like terms: 468 + 27.04 = 495.04 27.04 + -10.4x + x2 = 495.04 Factor a perfect square on the left side: (x + -5.2)(x + -5.2) = 495.04 Calculate the square root of the right side: 22.249494376 Break this problem into two subproblems by setting (x + -5.2) equal to 22.249494376 and -22.249494376.Subproblem 1
x + -5.2 = 22.249494376 Simplifying x + -5.2 = 22.249494376 Reorder the terms: -5.2 + x = 22.249494376 Solving -5.2 + x = 22.249494376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + x = 22.249494376 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = 22.249494376 + 5.2 x = 22.249494376 + 5.2 Combine like terms: 22.249494376 + 5.2 = 27.449494376 x = 27.449494376 Simplifying x = 27.449494376Subproblem 2
x + -5.2 = -22.249494376 Simplifying x + -5.2 = -22.249494376 Reorder the terms: -5.2 + x = -22.249494376 Solving -5.2 + x = -22.249494376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + x = -22.249494376 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = -22.249494376 + 5.2 x = -22.249494376 + 5.2 Combine like terms: -22.249494376 + 5.2 = -17.049494376 x = -17.049494376 Simplifying x = -17.049494376Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.449494376, -17.049494376}Solution
x = {27.449494376, -17.049494376}
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