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Simplifying 20.5x = 0.02x2 + 51.4 Reorder the terms: 20.5x = 51.4 + 0.02x2 Solving 20.5x = 51.4 + 0.02x2 Solving for variable 'x'. Reorder the terms: -51.4 + 20.5x + -0.02x2 = 51.4 + 0.02x2 + -51.4 + -0.02x2 Reorder the terms: -51.4 + 20.5x + -0.02x2 = 51.4 + -51.4 + 0.02x2 + -0.02x2 Combine like terms: 51.4 + -51.4 = 0.0 -51.4 + 20.5x + -0.02x2 = 0.0 + 0.02x2 + -0.02x2 -51.4 + 20.5x + -0.02x2 = 0.02x2 + -0.02x2 Combine like terms: 0.02x2 + -0.02x2 = 0.00 -51.4 + 20.5x + -0.02x2 = 0.00 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 2570 + -1025x + x2 = 0 Move the constant term to the right: Add '-2570' to each side of the equation. 2570 + -1025x + -2570 + x2 = 0 + -2570 Reorder the terms: 2570 + -2570 + -1025x + x2 = 0 + -2570 Combine like terms: 2570 + -2570 = 0 0 + -1025x + x2 = 0 + -2570 -1025x + x2 = 0 + -2570 Combine like terms: 0 + -2570 = -2570 -1025x + x2 = -2570 The x term is -1025x. Take half its coefficient (-512.5). Square it (262656.25) and add it to both sides. Add '262656.25' to each side of the equation. -1025x + 262656.25 + x2 = -2570 + 262656.25 Reorder the terms: 262656.25 + -1025x + x2 = -2570 + 262656.25 Combine like terms: -2570 + 262656.25 = 260086.25 262656.25 + -1025x + x2 = 260086.25 Factor a perfect square on the left side: (x + -512.5)(x + -512.5) = 260086.25 Calculate the square root of the right side: 509.98651943 Break this problem into two subproblems by setting (x + -512.5) equal to 509.98651943 and -509.98651943.Subproblem 1
x + -512.5 = 509.98651943 Simplifying x + -512.5 = 509.98651943 Reorder the terms: -512.5 + x = 509.98651943 Solving -512.5 + x = 509.98651943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '512.5' to each side of the equation. -512.5 + 512.5 + x = 509.98651943 + 512.5 Combine like terms: -512.5 + 512.5 = 0.0 0.0 + x = 509.98651943 + 512.5 x = 509.98651943 + 512.5 Combine like terms: 509.98651943 + 512.5 = 1022.48651943 x = 1022.48651943 Simplifying x = 1022.48651943Subproblem 2
x + -512.5 = -509.98651943 Simplifying x + -512.5 = -509.98651943 Reorder the terms: -512.5 + x = -509.98651943 Solving -512.5 + x = -509.98651943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '512.5' to each side of the equation. -512.5 + 512.5 + x = -509.98651943 + 512.5 Combine like terms: -512.5 + 512.5 = 0.0 0.0 + x = -509.98651943 + 512.5 x = -509.98651943 + 512.5 Combine like terms: -509.98651943 + 512.5 = 2.51348057 x = 2.51348057 Simplifying x = 2.51348057Solution
The solution to the problem is based on the solutions from the subproblems. x = {1022.48651943, 2.51348057}
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