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Simplifying 800 + -7x + -0.01x2 = 0 Solving 800 + -7x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -80000 + 700x + x2 = 0 Move the constant term to the right: Add '80000' to each side of the equation. -80000 + 700x + 80000 + x2 = 0 + 80000 Reorder the terms: -80000 + 80000 + 700x + x2 = 0 + 80000 Combine like terms: -80000 + 80000 = 0 0 + 700x + x2 = 0 + 80000 700x + x2 = 0 + 80000 Combine like terms: 0 + 80000 = 80000 700x + x2 = 80000 The x term is 700x. Take half its coefficient (350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. 700x + 122500 + x2 = 80000 + 122500 Reorder the terms: 122500 + 700x + x2 = 80000 + 122500 Combine like terms: 80000 + 122500 = 202500 122500 + 700x + x2 = 202500 Factor a perfect square on the left side: (x + 350)(x + 350) = 202500 Calculate the square root of the right side: 450 Break this problem into two subproblems by setting (x + 350) equal to 450 and -450.Subproblem 1
x + 350 = 450 Simplifying x + 350 = 450 Reorder the terms: 350 + x = 450 Solving 350 + x = 450 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = 450 + -350 Combine like terms: 350 + -350 = 0 0 + x = 450 + -350 x = 450 + -350 Combine like terms: 450 + -350 = 100 x = 100 Simplifying x = 100Subproblem 2
x + 350 = -450 Simplifying x + 350 = -450 Reorder the terms: 350 + x = -450 Solving 350 + x = -450 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = -450 + -350 Combine like terms: 350 + -350 = 0 0 + x = -450 + -350 x = -450 + -350 Combine like terms: -450 + -350 = -800 x = -800 Simplifying x = -800Solution
The solution to the problem is based on the solutions from the subproblems. x = {100, -800}
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