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Simplifying 25x2 + -37x = 570 Reorder the terms: -37x + 25x2 = 570 Solving -37x + 25x2 = 570 Solving for variable 'x'. Reorder the terms: -570 + -37x + 25x2 = 570 + -570 Combine like terms: 570 + -570 = 0 -570 + -37x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -22.8 + -1.48x + x2 = 0 Move the constant term to the right: Add '22.8' to each side of the equation. -22.8 + -1.48x + 22.8 + x2 = 0 + 22.8 Reorder the terms: -22.8 + 22.8 + -1.48x + x2 = 0 + 22.8 Combine like terms: -22.8 + 22.8 = 0.0 0.0 + -1.48x + x2 = 0 + 22.8 -1.48x + x2 = 0 + 22.8 Combine like terms: 0 + 22.8 = 22.8 -1.48x + x2 = 22.8 The x term is -1.48x. Take half its coefficient (-0.74). Square it (0.5476) and add it to both sides. Add '0.5476' to each side of the equation. -1.48x + 0.5476 + x2 = 22.8 + 0.5476 Reorder the terms: 0.5476 + -1.48x + x2 = 22.8 + 0.5476 Combine like terms: 22.8 + 0.5476 = 23.3476 0.5476 + -1.48x + x2 = 23.3476 Factor a perfect square on the left side: (x + -0.74)(x + -0.74) = 23.3476 Calculate the square root of the right side: 4.83193543 Break this problem into two subproblems by setting (x + -0.74) equal to 4.83193543 and -4.83193543.Subproblem 1
x + -0.74 = 4.83193543 Simplifying x + -0.74 = 4.83193543 Reorder the terms: -0.74 + x = 4.83193543 Solving -0.74 + x = 4.83193543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.74' to each side of the equation. -0.74 + 0.74 + x = 4.83193543 + 0.74 Combine like terms: -0.74 + 0.74 = 0.00 0.00 + x = 4.83193543 + 0.74 x = 4.83193543 + 0.74 Combine like terms: 4.83193543 + 0.74 = 5.57193543 x = 5.57193543 Simplifying x = 5.57193543Subproblem 2
x + -0.74 = -4.83193543 Simplifying x + -0.74 = -4.83193543 Reorder the terms: -0.74 + x = -4.83193543 Solving -0.74 + x = -4.83193543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.74' to each side of the equation. -0.74 + 0.74 + x = -4.83193543 + 0.74 Combine like terms: -0.74 + 0.74 = 0.00 0.00 + x = -4.83193543 + 0.74 x = -4.83193543 + 0.74 Combine like terms: -4.83193543 + 0.74 = -4.09193543 x = -4.09193543 Simplifying x = -4.09193543Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.57193543, -4.09193543}
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