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Simplifying 0.40x2 + -6x + -7000 = 0 Reorder the terms: -7000 + -6x + 0.40x2 = 0 Solving -7000 + -6x + 0.40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.40 the coefficient of the squared term: Divide each side by '0.40'. -17500 + -15x + x2 = 0 Move the constant term to the right: Add '17500' to each side of the equation. -17500 + -15x + 17500 + x2 = 0 + 17500 Reorder the terms: -17500 + 17500 + -15x + x2 = 0 + 17500 Combine like terms: -17500 + 17500 = 0 0 + -15x + x2 = 0 + 17500 -15x + x2 = 0 + 17500 Combine like terms: 0 + 17500 = 17500 -15x + x2 = 17500 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 17500 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 17500 + 56.25 Combine like terms: 17500 + 56.25 = 17556.25 56.25 + -15x + x2 = 17556.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 17556.25 Calculate the square root of the right side: 132.5 Break this problem into two subproblems by setting (x + -7.5) equal to 132.5 and -132.5.Subproblem 1
x + -7.5 = 132.5 Simplifying x + -7.5 = 132.5 Reorder the terms: -7.5 + x = 132.5 Solving -7.5 + x = 132.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 132.5 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 132.5 + 7.5 x = 132.5 + 7.5 Combine like terms: 132.5 + 7.5 = 140 x = 140 Simplifying x = 140Subproblem 2
x + -7.5 = -132.5 Simplifying x + -7.5 = -132.5 Reorder the terms: -7.5 + x = -132.5 Solving -7.5 + x = -132.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -132.5 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -132.5 + 7.5 x = -132.5 + 7.5 Combine like terms: -132.5 + 7.5 = -125 x = -125 Simplifying x = -125Solution
The solution to the problem is based on the solutions from the subproblems. x = {140, -125}
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