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Simplifying 160 + -7x = x2 + 15x Reorder the terms: 160 + -7x = 15x + x2 Solving 160 + -7x = 15x + x2 Solving for variable 'x'. Combine like terms: -7x + -15x = -22x 160 + -22x + -1x2 = 15x + x2 + -15x + -1x2 Reorder the terms: 160 + -22x + -1x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 160 + -22x + -1x2 = 0 + x2 + -1x2 160 + -22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 160 + -22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -160 + 22x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 22x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 22x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 22x + x2 = 0 + 160 22x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 22x + x2 = 160 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 160 + 121 Reorder the terms: 121 + 22x + x2 = 160 + 121 Combine like terms: 160 + 121 = 281 121 + 22x + x2 = 281 Factor a perfect square on the left side: (x + 11)(x + 11) = 281 Calculate the square root of the right side: 16.763054614 Break this problem into two subproblems by setting (x + 11) equal to 16.763054614 and -16.763054614.Subproblem 1
x + 11 = 16.763054614 Simplifying x + 11 = 16.763054614 Reorder the terms: 11 + x = 16.763054614 Solving 11 + x = 16.763054614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 16.763054614 + -11 Combine like terms: 11 + -11 = 0 0 + x = 16.763054614 + -11 x = 16.763054614 + -11 Combine like terms: 16.763054614 + -11 = 5.763054614 x = 5.763054614 Simplifying x = 5.763054614Subproblem 2
x + 11 = -16.763054614 Simplifying x + 11 = -16.763054614 Reorder the terms: 11 + x = -16.763054614 Solving 11 + x = -16.763054614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -16.763054614 + -11 Combine like terms: 11 + -11 = 0 0 + x = -16.763054614 + -11 x = -16.763054614 + -11 Combine like terms: -16.763054614 + -11 = -27.763054614 x = -27.763054614 Simplifying x = -27.763054614Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.763054614, -27.763054614}
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