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Simplifying 0.08x + 0.09x(x + 2000) = 690 Reorder the terms: 0.08x + 0.09x(2000 + x) = 690 0.08x + (2000 * 0.09x + x * 0.09x) = 690 0.08x + (180x + 0.09x2) = 690 Combine like terms: 0.08x + 180x = 180.08x 180.08x + 0.09x2 = 690 Solving 180.08x + 0.09x2 = 690 Solving for variable 'x'. Reorder the terms: -690 + 180.08x + 0.09x2 = 690 + -690 Combine like terms: 690 + -690 = 0 -690 + 180.08x + 0.09x2 = 0 Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. -7666.666667 + 2000.888889x + x2 = 0 Move the constant term to the right: Add '7666.666667' to each side of the equation. -7666.666667 + 2000.888889x + 7666.666667 + x2 = 0 + 7666.666667 Reorder the terms: -7666.666667 + 7666.666667 + 2000.888889x + x2 = 0 + 7666.666667 Combine like terms: -7666.666667 + 7666.666667 = 0.000000 0.000000 + 2000.888889x + x2 = 0 + 7666.666667 2000.888889x + x2 = 0 + 7666.666667 Combine like terms: 0 + 7666.666667 = 7666.666667 2000.888889x + x2 = 7666.666667 The x term is 2000.888889x. Take half its coefficient (1000.444445). Square it (1000889.088) and add it to both sides. Add '1000889.088' to each side of the equation. 2000.888889x + 1000889.088 + x2 = 7666.666667 + 1000889.088 Reorder the terms: 1000889.088 + 2000.888889x + x2 = 7666.666667 + 1000889.088 Combine like terms: 7666.666667 + 1000889.088 = 1008555.754667 1000889.088 + 2000.888889x + x2 = 1008555.754667 Factor a perfect square on the left side: (x + 1000.444445)(x + 1000.444445) = 1008555.754667 Calculate the square root of the right side: 1004.268766151 Break this problem into two subproblems by setting (x + 1000.444445) equal to 1004.268766151 and -1004.268766151.Subproblem 1
x + 1000.444445 = 1004.268766151 Simplifying x + 1000.444445 = 1004.268766151 Reorder the terms: 1000.444445 + x = 1004.268766151 Solving 1000.444445 + x = 1004.268766151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1000.444445' to each side of the equation. 1000.444445 + -1000.444445 + x = 1004.268766151 + -1000.444445 Combine like terms: 1000.444445 + -1000.444445 = 0.000000 0.000000 + x = 1004.268766151 + -1000.444445 x = 1004.268766151 + -1000.444445 Combine like terms: 1004.268766151 + -1000.444445 = 3.824321151 x = 3.824321151 Simplifying x = 3.824321151Subproblem 2
x + 1000.444445 = -1004.268766151 Simplifying x + 1000.444445 = -1004.268766151 Reorder the terms: 1000.444445 + x = -1004.268766151 Solving 1000.444445 + x = -1004.268766151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1000.444445' to each side of the equation. 1000.444445 + -1000.444445 + x = -1004.268766151 + -1000.444445 Combine like terms: 1000.444445 + -1000.444445 = 0.000000 0.000000 + x = -1004.268766151 + -1000.444445 x = -1004.268766151 + -1000.444445 Combine like terms: -1004.268766151 + -1000.444445 = -2004.713211151 x = -2004.713211151 Simplifying x = -2004.713211151Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.824321151, -2004.713211151}
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