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Simplifying (x + -600)(x + -600) * 0.04 + 40 = 6800 Reorder the terms: (-600 + x)(x + -600) * 0.04 + 40 = 6800 Reorder the terms: (-600 + x)(-600 + x) * 0.04 + 40 = 6800 Reorder the terms for easier multiplication: 0.04(-600 + x)(-600 + x) + 40 = 6800 Multiply (-600 + x) * (-600 + x) 0.04(-600(-600 + x) + x(-600 + x)) + 40 = 6800 0.04((-600 * -600 + x * -600) + x(-600 + x)) + 40 = 6800 0.04((360000 + -600x) + x(-600 + x)) + 40 = 6800 0.04(360000 + -600x + (-600 * x + x * x)) + 40 = 6800 0.04(360000 + -600x + (-600x + x2)) + 40 = 6800 Combine like terms: -600x + -600x = -1200x 0.04(360000 + -1200x + x2) + 40 = 6800 (360000 * 0.04 + -1200x * 0.04 + x2 * 0.04) + 40 = 6800 (14400 + -48x + 0.04x2) + 40 = 6800 Reorder the terms: 14400 + 40 + -48x + 0.04x2 = 6800 Combine like terms: 14400 + 40 = 14440 14440 + -48x + 0.04x2 = 6800 Solving 14440 + -48x + 0.04x2 = 6800 Solving for variable 'x'. Reorder the terms: 14440 + -6800 + -48x + 0.04x2 = 6800 + -6800 Combine like terms: 14440 + -6800 = 7640 7640 + -48x + 0.04x2 = 6800 + -6800 Combine like terms: 6800 + -6800 = 0 7640 + -48x + 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'. 191000 + -1200x + x2 = 0 Move the constant term to the right: Add '-191000' to each side of the equation. 191000 + -1200x + -191000 + x2 = 0 + -191000 Reorder the terms: 191000 + -191000 + -1200x + x2 = 0 + -191000 Combine like terms: 191000 + -191000 = 0 0 + -1200x + x2 = 0 + -191000 -1200x + x2 = 0 + -191000 Combine like terms: 0 + -191000 = -191000 -1200x + x2 = -191000 The x term is -1200x. Take half its coefficient (-600). Square it (360000) and add it to both sides. Add '360000' to each side of the equation. -1200x + 360000 + x2 = -191000 + 360000 Reorder the terms: 360000 + -1200x + x2 = -191000 + 360000 Combine like terms: -191000 + 360000 = 169000 360000 + -1200x + x2 = 169000 Factor a perfect square on the left side: (x + -600)(x + -600) = 169000 Calculate the square root of the right side: 411.096095822 Break this problem into two subproblems by setting (x + -600) equal to 411.096095822 and -411.096095822.Subproblem 1
x + -600 = 411.096095822 Simplifying x + -600 = 411.096095822 Reorder the terms: -600 + x = 411.096095822 Solving -600 + x = 411.096095822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '600' to each side of the equation. -600 + 600 + x = 411.096095822 + 600 Combine like terms: -600 + 600 = 0 0 + x = 411.096095822 + 600 x = 411.096095822 + 600 Combine like terms: 411.096095822 + 600 = 1011.096095822 x = 1011.096095822 Simplifying x = 1011.096095822Subproblem 2
x + -600 = -411.096095822 Simplifying x + -600 = -411.096095822 Reorder the terms: -600 + x = -411.096095822 Solving -600 + x = -411.096095822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '600' to each side of the equation. -600 + 600 + x = -411.096095822 + 600 Combine like terms: -600 + 600 = 0 0 + x = -411.096095822 + 600 x = -411.096095822 + 600 Combine like terms: -411.096095822 + 600 = 188.903904178 x = 188.903904178 Simplifying x = 188.903904178Solution
The solution to the problem is based on the solutions from the subproblems. x = {1011.096095822, 188.903904178}
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