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Simplifying 0.07x + 0.04x(110000 + -1x) = 660 0.07x + (110000 * 0.04x + -1x * 0.04x) = 660 0.07x + (4400x + -0.04x2) = 660 Combine like terms: 0.07x + 4400x = 4400.07x 4400.07x + -0.04x2 = 660 Solving 4400.07x + -0.04x2 = 660 Solving for variable 'x'. Reorder the terms: -660 + 4400.07x + -0.04x2 = 660 + -660 Combine like terms: 660 + -660 = 0 -660 + 4400.07x + -0.04x2 = 0 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. 16500 + -110001.75x + x2 = 0 Move the constant term to the right: Add '-16500' to each side of the equation. 16500 + -110001.75x + -16500 + x2 = 0 + -16500 Reorder the terms: 16500 + -16500 + -110001.75x + x2 = 0 + -16500 Combine like terms: 16500 + -16500 = 0 0 + -110001.75x + x2 = 0 + -16500 -110001.75x + x2 = 0 + -16500 Combine like terms: 0 + -16500 = -16500 -110001.75x + x2 = -16500 The x term is -110001.75x. Take half its coefficient (-55000.875). Square it (3025096251) and add it to both sides. Add '3025096251' to each side of the equation. -110001.75x + 3025096251 + x2 = -16500 + 3025096251 Reorder the terms: 3025096251 + -110001.75x + x2 = -16500 + 3025096251 Combine like terms: -16500 + 3025096251 = 3025079751 3025096251 + -110001.75x + x2 = 3025079751 Factor a perfect square on the left side: (x + -55000.875)(x + -55000.875) = 3025079751 Calculate the square root of the right side: 55000.725004312 Break this problem into two subproblems by setting (x + -55000.875) equal to 55000.725004312 and -55000.725004312.Subproblem 1
x + -55000.875 = 55000.725004312 Simplifying x + -55000.875 = 55000.725004312 Reorder the terms: -55000.875 + x = 55000.725004312 Solving -55000.875 + x = 55000.725004312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55000.875' to each side of the equation. -55000.875 + 55000.875 + x = 55000.725004312 + 55000.875 Combine like terms: -55000.875 + 55000.875 = 0.000 0.000 + x = 55000.725004312 + 55000.875 x = 55000.725004312 + 55000.875 Combine like terms: 55000.725004312 + 55000.875 = 110001.600004312 x = 110001.600004312 Simplifying x = 110001.600004312Subproblem 2
x + -55000.875 = -55000.725004312 Simplifying x + -55000.875 = -55000.725004312 Reorder the terms: -55000.875 + x = -55000.725004312 Solving -55000.875 + x = -55000.725004312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55000.875' to each side of the equation. -55000.875 + 55000.875 + x = -55000.725004312 + 55000.875 Combine like terms: -55000.875 + 55000.875 = 0.000 0.000 + x = -55000.725004312 + 55000.875 x = -55000.725004312 + 55000.875 Combine like terms: -55000.725004312 + 55000.875 = 0.149995688 x = 0.149995688 Simplifying x = 0.149995688Solution
The solution to the problem is based on the solutions from the subproblems. x = {110001.600004312, 0.149995688}
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