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Simplifying 91000 = 35x2 + -3640x + 7000 Reorder the terms: 91000 = 7000 + -3640x + 35x2 Solving 91000 = 7000 + -3640x + 35x2 Solving for variable 'x'. Combine like terms: 91000 + -7000 = 84000 84000 + 3640x + -35x2 = 7000 + -3640x + 35x2 + -7000 + 3640x + -35x2 Reorder the terms: 84000 + 3640x + -35x2 = 7000 + -7000 + -3640x + 3640x + 35x2 + -35x2 Combine like terms: 7000 + -7000 = 0 84000 + 3640x + -35x2 = 0 + -3640x + 3640x + 35x2 + -35x2 84000 + 3640x + -35x2 = -3640x + 3640x + 35x2 + -35x2 Combine like terms: -3640x + 3640x = 0 84000 + 3640x + -35x2 = 0 + 35x2 + -35x2 84000 + 3640x + -35x2 = 35x2 + -35x2 Combine like terms: 35x2 + -35x2 = 0 84000 + 3640x + -35x2 = 0 Factor out the Greatest Common Factor (GCF), '35'. 35(2400 + 104x + -1x2) = 0 Ignore the factor 35.Subproblem 1
Set the factor '(2400 + 104x + -1x2)' equal to zero and attempt to solve: Simplifying 2400 + 104x + -1x2 = 0 Solving 2400 + 104x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2400 + -104x + x2 = 0 Move the constant term to the right: Add '2400' to each side of the equation. -2400 + -104x + 2400 + x2 = 0 + 2400 Reorder the terms: -2400 + 2400 + -104x + x2 = 0 + 2400 Combine like terms: -2400 + 2400 = 0 0 + -104x + x2 = 0 + 2400 -104x + x2 = 0 + 2400 Combine like terms: 0 + 2400 = 2400 -104x + x2 = 2400 The x term is -104x. Take half its coefficient (-52). Square it (2704) and add it to both sides. Add '2704' to each side of the equation. -104x + 2704 + x2 = 2400 + 2704 Reorder the terms: 2704 + -104x + x2 = 2400 + 2704 Combine like terms: 2400 + 2704 = 5104 2704 + -104x + x2 = 5104 Factor a perfect square on the left side: (x + -52)(x + -52) = 5104 Calculate the square root of the right side: 71.442284398 Break this problem into two subproblems by setting (x + -52) equal to 71.442284398 and -71.442284398.Subproblem 1
x + -52 = 71.442284398 Simplifying x + -52 = 71.442284398 Reorder the terms: -52 + x = 71.442284398 Solving -52 + x = 71.442284398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + x = 71.442284398 + 52 Combine like terms: -52 + 52 = 0 0 + x = 71.442284398 + 52 x = 71.442284398 + 52 Combine like terms: 71.442284398 + 52 = 123.442284398 x = 123.442284398 Simplifying x = 123.442284398Subproblem 2
x + -52 = -71.442284398 Simplifying x + -52 = -71.442284398 Reorder the terms: -52 + x = -71.442284398 Solving -52 + x = -71.442284398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + x = -71.442284398 + 52 Combine like terms: -52 + 52 = 0 0 + x = -71.442284398 + 52 x = -71.442284398 + 52 Combine like terms: -71.442284398 + 52 = -19.442284398 x = -19.442284398 Simplifying x = -19.442284398Solution
The solution to the problem is based on the solutions from the subproblems. x = {123.442284398, -19.442284398}Solution
x = {123.442284398, -19.442284398}
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