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Simplifying 9x2 + -3500x + 150000 = 0 Reorder the terms: 150000 + -3500x + 9x2 = 0 Solving 150000 + -3500x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 16666.66667 + -388.8888889x + x2 = 0 Move the constant term to the right: Add '-16666.66667' to each side of the equation. 16666.66667 + -388.8888889x + -16666.66667 + x2 = 0 + -16666.66667 Reorder the terms: 16666.66667 + -16666.66667 + -388.8888889x + x2 = 0 + -16666.66667 Combine like terms: 16666.66667 + -16666.66667 = 0.00000 0.00000 + -388.8888889x + x2 = 0 + -16666.66667 -388.8888889x + x2 = 0 + -16666.66667 Combine like terms: 0 + -16666.66667 = -16666.66667 -388.8888889x + x2 = -16666.66667 The x term is -388.8888889x. Take half its coefficient (-194.4444445). Square it (37808.64200) and add it to both sides. Add '37808.64200' to each side of the equation. -388.8888889x + 37808.64200 + x2 = -16666.66667 + 37808.64200 Reorder the terms: 37808.64200 + -388.8888889x + x2 = -16666.66667 + 37808.64200 Combine like terms: -16666.66667 + 37808.64200 = 21141.97533 37808.64200 + -388.8888889x + x2 = 21141.97533 Factor a perfect square on the left side: (x + -194.4444445)(x + -194.4444445) = 21141.97533 Calculate the square root of the right side: 145.402803721 Break this problem into two subproblems by setting (x + -194.4444445) equal to 145.402803721 and -145.402803721.Subproblem 1
x + -194.4444445 = 145.402803721 Simplifying x + -194.4444445 = 145.402803721 Reorder the terms: -194.4444445 + x = 145.402803721 Solving -194.4444445 + x = 145.402803721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '194.4444445' to each side of the equation. -194.4444445 + 194.4444445 + x = 145.402803721 + 194.4444445 Combine like terms: -194.4444445 + 194.4444445 = 0.0000000 0.0000000 + x = 145.402803721 + 194.4444445 x = 145.402803721 + 194.4444445 Combine like terms: 145.402803721 + 194.4444445 = 339.847248221 x = 339.847248221 Simplifying x = 339.847248221Subproblem 2
x + -194.4444445 = -145.402803721 Simplifying x + -194.4444445 = -145.402803721 Reorder the terms: -194.4444445 + x = -145.402803721 Solving -194.4444445 + x = -145.402803721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '194.4444445' to each side of the equation. -194.4444445 + 194.4444445 + x = -145.402803721 + 194.4444445 Combine like terms: -194.4444445 + 194.4444445 = 0.0000000 0.0000000 + x = -145.402803721 + 194.4444445 x = -145.402803721 + 194.4444445 Combine like terms: -145.402803721 + 194.4444445 = 49.041640779 x = 49.041640779 Simplifying x = 49.041640779Solution
The solution to the problem is based on the solutions from the subproblems. x = {339.847248221, 49.041640779}
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