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Simplifying 150x + -1(2800 + 7x + 0.1x2) = 0 150x + (2800 * -1 + 7x * -1 + 0.1x2 * -1) = 0 150x + (-2800 + -7x + -0.1x2) = 0 Reorder the terms: -2800 + 150x + -7x + -0.1x2 = 0 Combine like terms: 150x + -7x = 143x -2800 + 143x + -0.1x2 = 0 Solving -2800 + 143x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 28000 + -1430x + x2 = 0 Move the constant term to the right: Add '-28000' to each side of the equation. 28000 + -1430x + -28000 + x2 = 0 + -28000 Reorder the terms: 28000 + -28000 + -1430x + x2 = 0 + -28000 Combine like terms: 28000 + -28000 = 0 0 + -1430x + x2 = 0 + -28000 -1430x + x2 = 0 + -28000 Combine like terms: 0 + -28000 = -28000 -1430x + x2 = -28000 The x term is -1430x. Take half its coefficient (-715). Square it (511225) and add it to both sides. Add '511225' to each side of the equation. -1430x + 511225 + x2 = -28000 + 511225 Reorder the terms: 511225 + -1430x + x2 = -28000 + 511225 Combine like terms: -28000 + 511225 = 483225 511225 + -1430x + x2 = 483225 Factor a perfect square on the left side: (x + -715)(x + -715) = 483225 Calculate the square root of the right side: 695.143870001 Break this problem into two subproblems by setting (x + -715) equal to 695.143870001 and -695.143870001.Subproblem 1
x + -715 = 695.143870001 Simplifying x + -715 = 695.143870001 Reorder the terms: -715 + x = 695.143870001 Solving -715 + x = 695.143870001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '715' to each side of the equation. -715 + 715 + x = 695.143870001 + 715 Combine like terms: -715 + 715 = 0 0 + x = 695.143870001 + 715 x = 695.143870001 + 715 Combine like terms: 695.143870001 + 715 = 1410.143870001 x = 1410.143870001 Simplifying x = 1410.143870001Subproblem 2
x + -715 = -695.143870001 Simplifying x + -715 = -695.143870001 Reorder the terms: -715 + x = -695.143870001 Solving -715 + x = -695.143870001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '715' to each side of the equation. -715 + 715 + x = -695.143870001 + 715 Combine like terms: -715 + 715 = 0 0 + x = -695.143870001 + 715 x = -695.143870001 + 715 Combine like terms: -695.143870001 + 715 = 19.856129999 x = 19.856129999 Simplifying x = 19.856129999Solution
The solution to the problem is based on the solutions from the subproblems. x = {1410.143870001, 19.856129999}
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