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Simplifying 4x2 + -288x + 59 = 0 Reorder the terms: 59 + -288x + 4x2 = 0 Solving 59 + -288x + 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'. 14.75 + -72x + x2 = 0 Move the constant term to the right: Add '-14.75' to each side of the equation. 14.75 + -72x + -14.75 + x2 = 0 + -14.75 Reorder the terms: 14.75 + -14.75 + -72x + x2 = 0 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + -72x + x2 = 0 + -14.75 -72x + x2 = 0 + -14.75 Combine like terms: 0 + -14.75 = -14.75 -72x + x2 = -14.75 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = -14.75 + 1296 Reorder the terms: 1296 + -72x + x2 = -14.75 + 1296 Combine like terms: -14.75 + 1296 = 1281.25 1296 + -72x + x2 = 1281.25 Factor a perfect square on the left side: (x + -36)(x + -36) = 1281.25 Calculate the square root of the right side: 35.794552658 Break this problem into two subproblems by setting (x + -36) equal to 35.794552658 and -35.794552658.Subproblem 1
x + -36 = 35.794552658 Simplifying x + -36 = 35.794552658 Reorder the terms: -36 + x = 35.794552658 Solving -36 + x = 35.794552658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 35.794552658 + 36 Combine like terms: -36 + 36 = 0 0 + x = 35.794552658 + 36 x = 35.794552658 + 36 Combine like terms: 35.794552658 + 36 = 71.794552658 x = 71.794552658 Simplifying x = 71.794552658Subproblem 2
x + -36 = -35.794552658 Simplifying x + -36 = -35.794552658 Reorder the terms: -36 + x = -35.794552658 Solving -36 + x = -35.794552658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -35.794552658 + 36 Combine like terms: -36 + 36 = 0 0 + x = -35.794552658 + 36 x = -35.794552658 + 36 Combine like terms: -35.794552658 + 36 = 0.205447342 x = 0.205447342 Simplifying x = 0.205447342Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.794552658, 0.205447342}
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