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Simplifying 5x2 + -6x + -500 = 0 Reorder the terms: -500 + -6x + 5x2 = 0 Solving -500 + -6x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -100 + -1.2x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -1.2x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -1.2x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -1.2x + x2 = 0 + 100 -1.2x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -1.2x + x2 = 100 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 100 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 100 + 0.36 Combine like terms: 100 + 0.36 = 100.36 0.36 + -1.2x + x2 = 100.36 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 100.36 Calculate the square root of the right side: 10.017983829 Break this problem into two subproblems by setting (x + -0.6) equal to 10.017983829 and -10.017983829.Subproblem 1
x + -0.6 = 10.017983829 Simplifying x + -0.6 = 10.017983829 Reorder the terms: -0.6 + x = 10.017983829 Solving -0.6 + x = 10.017983829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 10.017983829 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 10.017983829 + 0.6 x = 10.017983829 + 0.6 Combine like terms: 10.017983829 + 0.6 = 10.617983829 x = 10.617983829 Simplifying x = 10.617983829Subproblem 2
x + -0.6 = -10.017983829 Simplifying x + -0.6 = -10.017983829 Reorder the terms: -0.6 + x = -10.017983829 Solving -0.6 + x = -10.017983829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -10.017983829 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -10.017983829 + 0.6 x = -10.017983829 + 0.6 Combine like terms: -10.017983829 + 0.6 = -9.417983829 x = -9.417983829 Simplifying x = -9.417983829Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.617983829, -9.417983829}
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