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Simplifying -10x2 + 225x + 2900 = 0 Reorder the terms: 2900 + 225x + -10x2 = 0 Solving 2900 + 225x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(580 + 45x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(580 + 45x + -2x2)' equal to zero and attempt to solve: Simplifying 580 + 45x + -2x2 = 0 Solving 580 + 45x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -290 + -22.5x + x2 = 0 Move the constant term to the right: Add '290' to each side of the equation. -290 + -22.5x + 290 + x2 = 0 + 290 Reorder the terms: -290 + 290 + -22.5x + x2 = 0 + 290 Combine like terms: -290 + 290 = 0 0 + -22.5x + x2 = 0 + 290 -22.5x + x2 = 0 + 290 Combine like terms: 0 + 290 = 290 -22.5x + x2 = 290 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = 290 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = 290 + 126.5625 Combine like terms: 290 + 126.5625 = 416.5625 126.5625 + -22.5x + x2 = 416.5625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 416.5625 Calculate the square root of the right side: 20.409862812 Break this problem into two subproblems by setting (x + -11.25) equal to 20.409862812 and -20.409862812.Subproblem 1
x + -11.25 = 20.409862812 Simplifying x + -11.25 = 20.409862812 Reorder the terms: -11.25 + x = 20.409862812 Solving -11.25 + x = 20.409862812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 20.409862812 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 20.409862812 + 11.25 x = 20.409862812 + 11.25 Combine like terms: 20.409862812 + 11.25 = 31.659862812 x = 31.659862812 Simplifying x = 31.659862812Subproblem 2
x + -11.25 = -20.409862812 Simplifying x + -11.25 = -20.409862812 Reorder the terms: -11.25 + x = -20.409862812 Solving -11.25 + x = -20.409862812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -20.409862812 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -20.409862812 + 11.25 x = -20.409862812 + 11.25 Combine like terms: -20.409862812 + 11.25 = -9.159862812 x = -9.159862812 Simplifying x = -9.159862812Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.659862812, -9.159862812}Solution
x = {31.659862812, -9.159862812}
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