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Simplifying 4x2 + -69x + -287 = 0 Reorder the terms: -287 + -69x + 4x2 = 0 Solving -287 + -69x + 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'. -71.75 + -17.25x + x2 = 0 Move the constant term to the right: Add '71.75' to each side of the equation. -71.75 + -17.25x + 71.75 + x2 = 0 + 71.75 Reorder the terms: -71.75 + 71.75 + -17.25x + x2 = 0 + 71.75 Combine like terms: -71.75 + 71.75 = 0.00 0.00 + -17.25x + x2 = 0 + 71.75 -17.25x + x2 = 0 + 71.75 Combine like terms: 0 + 71.75 = 71.75 -17.25x + x2 = 71.75 The x term is -17.25x. Take half its coefficient (-8.625). Square it (74.390625) and add it to both sides. Add '74.390625' to each side of the equation. -17.25x + 74.390625 + x2 = 71.75 + 74.390625 Reorder the terms: 74.390625 + -17.25x + x2 = 71.75 + 74.390625 Combine like terms: 71.75 + 74.390625 = 146.140625 74.390625 + -17.25x + x2 = 146.140625 Factor a perfect square on the left side: (x + -8.625)(x + -8.625) = 146.140625 Calculate the square root of the right side: 12.088863677 Break this problem into two subproblems by setting (x + -8.625) equal to 12.088863677 and -12.088863677.Subproblem 1
x + -8.625 = 12.088863677 Simplifying x + -8.625 = 12.088863677 Reorder the terms: -8.625 + x = 12.088863677 Solving -8.625 + x = 12.088863677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.625' to each side of the equation. -8.625 + 8.625 + x = 12.088863677 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + x = 12.088863677 + 8.625 x = 12.088863677 + 8.625 Combine like terms: 12.088863677 + 8.625 = 20.713863677 x = 20.713863677 Simplifying x = 20.713863677Subproblem 2
x + -8.625 = -12.088863677 Simplifying x + -8.625 = -12.088863677 Reorder the terms: -8.625 + x = -12.088863677 Solving -8.625 + x = -12.088863677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.625' to each side of the equation. -8.625 + 8.625 + x = -12.088863677 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + x = -12.088863677 + 8.625 x = -12.088863677 + 8.625 Combine like terms: -12.088863677 + 8.625 = -3.463863677 x = -3.463863677 Simplifying x = -3.463863677Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.713863677, -3.463863677}
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