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Simplifying 10x2 + -50x + -3 = 0 Reorder the terms: -3 + -50x + 10x2 = 0 Solving -3 + -50x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -5x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -5x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -5x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -5x + x2 = 0 + 0.3 -5x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -5x + x2 = 0.3 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.3 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.3 + 6.25 Combine like terms: 0.3 + 6.25 = 6.55 6.25 + -5x + x2 = 6.55 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.55 Calculate the square root of the right side: 2.559296778 Break this problem into two subproblems by setting (x + -2.5) equal to 2.559296778 and -2.559296778.Subproblem 1
x + -2.5 = 2.559296778 Simplifying x + -2.5 = 2.559296778 Reorder the terms: -2.5 + x = 2.559296778 Solving -2.5 + x = 2.559296778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.559296778 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.559296778 + 2.5 x = 2.559296778 + 2.5 Combine like terms: 2.559296778 + 2.5 = 5.059296778 x = 5.059296778 Simplifying x = 5.059296778Subproblem 2
x + -2.5 = -2.559296778 Simplifying x + -2.5 = -2.559296778 Reorder the terms: -2.5 + x = -2.559296778 Solving -2.5 + x = -2.559296778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.559296778 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.559296778 + 2.5 x = -2.559296778 + 2.5 Combine like terms: -2.559296778 + 2.5 = -0.059296778 x = -0.059296778 Simplifying x = -0.059296778Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.059296778, -0.059296778}
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