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Simplifying 0 = 0.003x2 + 4.2x + 1000 Reorder the terms: 0 = 1000 + 4.2x + 0.003x2 Solving 0 = 1000 + 4.2x + 0.003x2 Solving for variable 'x'. Combine like terms: 0 + -1000 = -1000 -1000 + -4.2x + -0.003x2 = 1000 + 4.2x + 0.003x2 + -1000 + -4.2x + -0.003x2 Reorder the terms: -1000 + -4.2x + -0.003x2 = 1000 + -1000 + 4.2x + -4.2x + 0.003x2 + -0.003x2 Combine like terms: 1000 + -1000 = 0 -1000 + -4.2x + -0.003x2 = 0 + 4.2x + -4.2x + 0.003x2 + -0.003x2 -1000 + -4.2x + -0.003x2 = 4.2x + -4.2x + 0.003x2 + -0.003x2 Combine like terms: 4.2x + -4.2x = 0.0 -1000 + -4.2x + -0.003x2 = 0.0 + 0.003x2 + -0.003x2 -1000 + -4.2x + -0.003x2 = 0.003x2 + -0.003x2 Combine like terms: 0.003x2 + -0.003x2 = 0.000 -1000 + -4.2x + -0.003x2 = 0.000 Begin completing the square. Divide all terms by -0.003 the coefficient of the squared term: Divide each side by '-0.003'. 333333.3333 + 1400x + x2 = 0 Move the constant term to the right: Add '-333333.3333' to each side of the equation. 333333.3333 + 1400x + -333333.3333 + x2 = 0 + -333333.3333 Reorder the terms: 333333.3333 + -333333.3333 + 1400x + x2 = 0 + -333333.3333 Combine like terms: 333333.3333 + -333333.3333 = 0.0000 0.0000 + 1400x + x2 = 0 + -333333.3333 1400x + x2 = 0 + -333333.3333 Combine like terms: 0 + -333333.3333 = -333333.3333 1400x + x2 = -333333.3333 The x term is 1400x. Take half its coefficient (700). Square it (490000) and add it to both sides. Add '490000' to each side of the equation. 1400x + 490000 + x2 = -333333.3333 + 490000 Reorder the terms: 490000 + 1400x + x2 = -333333.3333 + 490000 Combine like terms: -333333.3333 + 490000 = 156666.6667 490000 + 1400x + x2 = 156666.6667 Factor a perfect square on the left side: (x + 700)(x + 700) = 156666.6667 Calculate the square root of the right side: 395.811402943 Break this problem into two subproblems by setting (x + 700) equal to 395.811402943 and -395.811402943.Subproblem 1
x + 700 = 395.811402943 Simplifying x + 700 = 395.811402943 Reorder the terms: 700 + x = 395.811402943 Solving 700 + x = 395.811402943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-700' to each side of the equation. 700 + -700 + x = 395.811402943 + -700 Combine like terms: 700 + -700 = 0 0 + x = 395.811402943 + -700 x = 395.811402943 + -700 Combine like terms: 395.811402943 + -700 = -304.188597057 x = -304.188597057 Simplifying x = -304.188597057Subproblem 2
x + 700 = -395.811402943 Simplifying x + 700 = -395.811402943 Reorder the terms: 700 + x = -395.811402943 Solving 700 + x = -395.811402943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-700' to each side of the equation. 700 + -700 + x = -395.811402943 + -700 Combine like terms: 700 + -700 = 0 0 + x = -395.811402943 + -700 x = -395.811402943 + -700 Combine like terms: -395.811402943 + -700 = -1095.811402943 x = -1095.811402943 Simplifying x = -1095.811402943Solution
The solution to the problem is based on the solutions from the subproblems. x = {-304.188597057, -1095.811402943}
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