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Simplifying 875 + -120x + -4x2 = 0 Solving 875 + -120x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -218.75 + 30x + x2 = 0 Move the constant term to the right: Add '218.75' to each side of the equation. -218.75 + 30x + 218.75 + x2 = 0 + 218.75 Reorder the terms: -218.75 + 218.75 + 30x + x2 = 0 + 218.75 Combine like terms: -218.75 + 218.75 = 0.00 0.00 + 30x + x2 = 0 + 218.75 30x + x2 = 0 + 218.75 Combine like terms: 0 + 218.75 = 218.75 30x + x2 = 218.75 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 218.75 + 225 Reorder the terms: 225 + 30x + x2 = 218.75 + 225 Combine like terms: 218.75 + 225 = 443.75 225 + 30x + x2 = 443.75 Factor a perfect square on the left side: (x + 15)(x + 15) = 443.75 Calculate the square root of the right side: 21.065374433 Break this problem into two subproblems by setting (x + 15) equal to 21.065374433 and -21.065374433.Subproblem 1
x + 15 = 21.065374433 Simplifying x + 15 = 21.065374433 Reorder the terms: 15 + x = 21.065374433 Solving 15 + x = 21.065374433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 21.065374433 + -15 Combine like terms: 15 + -15 = 0 0 + x = 21.065374433 + -15 x = 21.065374433 + -15 Combine like terms: 21.065374433 + -15 = 6.065374433 x = 6.065374433 Simplifying x = 6.065374433Subproblem 2
x + 15 = -21.065374433 Simplifying x + 15 = -21.065374433 Reorder the terms: 15 + x = -21.065374433 Solving 15 + x = -21.065374433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -21.065374433 + -15 Combine like terms: 15 + -15 = 0 0 + x = -21.065374433 + -15 x = -21.065374433 + -15 Combine like terms: -21.065374433 + -15 = -36.065374433 x = -36.065374433 Simplifying x = -36.065374433Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.065374433, -36.065374433}
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