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Simplifying 0.09x2 + -5x + -7000 = 0 Reorder the terms: -7000 + -5x + 0.09x2 = 0 Solving -7000 + -5x + 0.09x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. -77777.77778 + -55.55555556x + x2 = 0 Move the constant term to the right: Add '77777.77778' to each side of the equation. -77777.77778 + -55.55555556x + 77777.77778 + x2 = 0 + 77777.77778 Reorder the terms: -77777.77778 + 77777.77778 + -55.55555556x + x2 = 0 + 77777.77778 Combine like terms: -77777.77778 + 77777.77778 = 0.00000 0.00000 + -55.55555556x + x2 = 0 + 77777.77778 -55.55555556x + x2 = 0 + 77777.77778 Combine like terms: 0 + 77777.77778 = 77777.77778 -55.55555556x + x2 = 77777.77778 The x term is -55.55555556x. Take half its coefficient (-27.77777778). Square it (771.6049384) and add it to both sides. Add '771.6049384' to each side of the equation. -55.55555556x + 771.6049384 + x2 = 77777.77778 + 771.6049384 Reorder the terms: 771.6049384 + -55.55555556x + x2 = 77777.77778 + 771.6049384 Combine like terms: 77777.77778 + 771.6049384 = 78549.3827184 771.6049384 + -55.55555556x + x2 = 78549.3827184 Factor a perfect square on the left side: (x + -27.77777778)(x + -27.77777778) = 78549.3827184 Calculate the square root of the right side: 280.266627907 Break this problem into two subproblems by setting (x + -27.77777778) equal to 280.266627907 and -280.266627907.Subproblem 1
x + -27.77777778 = 280.266627907 Simplifying x + -27.77777778 = 280.266627907 Reorder the terms: -27.77777778 + x = 280.266627907 Solving -27.77777778 + x = 280.266627907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.77777778' to each side of the equation. -27.77777778 + 27.77777778 + x = 280.266627907 + 27.77777778 Combine like terms: -27.77777778 + 27.77777778 = 0.00000000 0.00000000 + x = 280.266627907 + 27.77777778 x = 280.266627907 + 27.77777778 Combine like terms: 280.266627907 + 27.77777778 = 308.044405687 x = 308.044405687 Simplifying x = 308.044405687Subproblem 2
x + -27.77777778 = -280.266627907 Simplifying x + -27.77777778 = -280.266627907 Reorder the terms: -27.77777778 + x = -280.266627907 Solving -27.77777778 + x = -280.266627907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.77777778' to each side of the equation. -27.77777778 + 27.77777778 + x = -280.266627907 + 27.77777778 Combine like terms: -27.77777778 + 27.77777778 = 0.00000000 0.00000000 + x = -280.266627907 + 27.77777778 x = -280.266627907 + 27.77777778 Combine like terms: -280.266627907 + 27.77777778 = -252.488850127 x = -252.488850127 Simplifying x = -252.488850127Solution
The solution to the problem is based on the solutions from the subproblems. x = {308.044405687, -252.488850127}
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