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Simplifying 2322x2 + 5164x + 5893 = 81000 Reorder the terms: 5893 + 5164x + 2322x2 = 81000 Solving 5893 + 5164x + 2322x2 = 81000 Solving for variable 'x'. Reorder the terms: 5893 + -81000 + 5164x + 2322x2 = 81000 + -81000 Combine like terms: 5893 + -81000 = -75107 -75107 + 5164x + 2322x2 = 81000 + -81000 Combine like terms: 81000 + -81000 = 0 -75107 + 5164x + 2322x2 = 0 Begin completing the square. Divide all terms by 2322 the coefficient of the squared term: Divide each side by '2322'. -32.34582257 + 2.223944875x + x2 = 0 Move the constant term to the right: Add '32.34582257' to each side of the equation. -32.34582257 + 2.223944875x + 32.34582257 + x2 = 0 + 32.34582257 Reorder the terms: -32.34582257 + 32.34582257 + 2.223944875x + x2 = 0 + 32.34582257 Combine like terms: -32.34582257 + 32.34582257 = 0.00000000 0.00000000 + 2.223944875x + x2 = 0 + 32.34582257 2.223944875x + x2 = 0 + 32.34582257 Combine like terms: 0 + 32.34582257 = 32.34582257 2.223944875x + x2 = 32.34582257 The x term is 2.223944875x. Take half its coefficient (1.111972438). Square it (1.236482703) and add it to both sides. Add '1.236482703' to each side of the equation. 2.223944875x + 1.236482703 + x2 = 32.34582257 + 1.236482703 Reorder the terms: 1.236482703 + 2.223944875x + x2 = 32.34582257 + 1.236482703 Combine like terms: 32.34582257 + 1.236482703 = 33.582305273 1.236482703 + 2.223944875x + x2 = 33.582305273 Factor a perfect square on the left side: (x + 1.111972438)(x + 1.111972438) = 33.582305273 Calculate the square root of the right side: 5.795024182 Break this problem into two subproblems by setting (x + 1.111972438) equal to 5.795024182 and -5.795024182.Subproblem 1
x + 1.111972438 = 5.795024182 Simplifying x + 1.111972438 = 5.795024182 Reorder the terms: 1.111972438 + x = 5.795024182 Solving 1.111972438 + x = 5.795024182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111972438' to each side of the equation. 1.111972438 + -1.111972438 + x = 5.795024182 + -1.111972438 Combine like terms: 1.111972438 + -1.111972438 = 0.000000000 0.000000000 + x = 5.795024182 + -1.111972438 x = 5.795024182 + -1.111972438 Combine like terms: 5.795024182 + -1.111972438 = 4.683051744 x = 4.683051744 Simplifying x = 4.683051744Subproblem 2
x + 1.111972438 = -5.795024182 Simplifying x + 1.111972438 = -5.795024182 Reorder the terms: 1.111972438 + x = -5.795024182 Solving 1.111972438 + x = -5.795024182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111972438' to each side of the equation. 1.111972438 + -1.111972438 + x = -5.795024182 + -1.111972438 Combine like terms: 1.111972438 + -1.111972438 = 0.000000000 0.000000000 + x = -5.795024182 + -1.111972438 x = -5.795024182 + -1.111972438 Combine like terms: -5.795024182 + -1.111972438 = -6.90699662 x = -6.90699662 Simplifying x = -6.90699662Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.683051744, -6.90699662}
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