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Simplifying -1x2 + 28x + -36 = 0 Reorder the terms: -36 + 28x + -1x2 = 0 Solving -36 + 28x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -28x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -28x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -28x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -28x + x2 = 0 + -36 -28x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -28x + x2 = -36 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -36 + 196 Reorder the terms: 196 + -28x + x2 = -36 + 196 Combine like terms: -36 + 196 = 160 196 + -28x + x2 = 160 Factor a perfect square on the left side: (x + -14)(x + -14) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + -14) equal to 12.649110641 and -12.649110641.Subproblem 1
x + -14 = 12.649110641 Simplifying x + -14 = 12.649110641 Reorder the terms: -14 + x = 12.649110641 Solving -14 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 12.649110641 + 14 Combine like terms: -14 + 14 = 0 0 + x = 12.649110641 + 14 x = 12.649110641 + 14 Combine like terms: 12.649110641 + 14 = 26.649110641 x = 26.649110641 Simplifying x = 26.649110641Subproblem 2
x + -14 = -12.649110641 Simplifying x + -14 = -12.649110641 Reorder the terms: -14 + x = -12.649110641 Solving -14 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -12.649110641 + 14 Combine like terms: -14 + 14 = 0 0 + x = -12.649110641 + 14 x = -12.649110641 + 14 Combine like terms: -12.649110641 + 14 = 1.350889359 x = 1.350889359 Simplifying x = 1.350889359Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.649110641, 1.350889359}
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