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Simplifying 10x2 + 6x + -39999 = 0 Reorder the terms: -39999 + 6x + 10x2 = 0 Solving -39999 + 6x + 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'. -3999.9 + 0.6x + x2 = 0 Move the constant term to the right: Add '3999.9' to each side of the equation. -3999.9 + 0.6x + 3999.9 + x2 = 0 + 3999.9 Reorder the terms: -3999.9 + 3999.9 + 0.6x + x2 = 0 + 3999.9 Combine like terms: -3999.9 + 3999.9 = 0.0 0.0 + 0.6x + x2 = 0 + 3999.9 0.6x + x2 = 0 + 3999.9 Combine like terms: 0 + 3999.9 = 3999.9 0.6x + x2 = 3999.9 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 3999.9 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 3999.9 + 0.09 Combine like terms: 3999.9 + 0.09 = 3999.99 0.09 + 0.6x + x2 = 3999.99 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 3999.99 Calculate the square root of the right side: 63.245474146 Break this problem into two subproblems by setting (x + 0.3) equal to 63.245474146 and -63.245474146.Subproblem 1
x + 0.3 = 63.245474146 Simplifying x + 0.3 = 63.245474146 Reorder the terms: 0.3 + x = 63.245474146 Solving 0.3 + x = 63.245474146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 63.245474146 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 63.245474146 + -0.3 x = 63.245474146 + -0.3 Combine like terms: 63.245474146 + -0.3 = 62.945474146 x = 62.945474146 Simplifying x = 62.945474146Subproblem 2
x + 0.3 = -63.245474146 Simplifying x + 0.3 = -63.245474146 Reorder the terms: 0.3 + x = -63.245474146 Solving 0.3 + x = -63.245474146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -63.245474146 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -63.245474146 + -0.3 x = -63.245474146 + -0.3 Combine like terms: -63.245474146 + -0.3 = -63.545474146 x = -63.545474146 Simplifying x = -63.545474146Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.945474146, -63.545474146}
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