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Simplifying -2x + 7x(5x + -17) = 13 Reorder the terms: -2x + 7x(-17 + 5x) = 13 -2x + (-17 * 7x + 5x * 7x) = 13 -2x + (-119x + 35x2) = 13 Combine like terms: -2x + -119x = -121x -121x + 35x2 = 13 Solving -121x + 35x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -121x + 35x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -121x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.3714285714 + -3.457142857x + x2 = 0 Move the constant term to the right: Add '0.3714285714' to each side of the equation. -0.3714285714 + -3.457142857x + 0.3714285714 + x2 = 0 + 0.3714285714 Reorder the terms: -0.3714285714 + 0.3714285714 + -3.457142857x + x2 = 0 + 0.3714285714 Combine like terms: -0.3714285714 + 0.3714285714 = 0.0000000000 0.0000000000 + -3.457142857x + x2 = 0 + 0.3714285714 -3.457142857x + x2 = 0 + 0.3714285714 Combine like terms: 0 + 0.3714285714 = 0.3714285714 -3.457142857x + x2 = 0.3714285714 The x term is -3.457142857x. Take half its coefficient (-1.728571429). Square it (2.987959185) and add it to both sides. Add '2.987959185' to each side of the equation. -3.457142857x + 2.987959185 + x2 = 0.3714285714 + 2.987959185 Reorder the terms: 2.987959185 + -3.457142857x + x2 = 0.3714285714 + 2.987959185 Combine like terms: 0.3714285714 + 2.987959185 = 3.3593877564 2.987959185 + -3.457142857x + x2 = 3.3593877564 Factor a perfect square on the left side: (x + -1.728571429)(x + -1.728571429) = 3.3593877564 Calculate the square root of the right side: 1.832863267 Break this problem into two subproblems by setting (x + -1.728571429) equal to 1.832863267 and -1.832863267.Subproblem 1
x + -1.728571429 = 1.832863267 Simplifying x + -1.728571429 = 1.832863267 Reorder the terms: -1.728571429 + x = 1.832863267 Solving -1.728571429 + x = 1.832863267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.728571429' to each side of the equation. -1.728571429 + 1.728571429 + x = 1.832863267 + 1.728571429 Combine like terms: -1.728571429 + 1.728571429 = 0.000000000 0.000000000 + x = 1.832863267 + 1.728571429 x = 1.832863267 + 1.728571429 Combine like terms: 1.832863267 + 1.728571429 = 3.561434696 x = 3.561434696 Simplifying x = 3.561434696Subproblem 2
x + -1.728571429 = -1.832863267 Simplifying x + -1.728571429 = -1.832863267 Reorder the terms: -1.728571429 + x = -1.832863267 Solving -1.728571429 + x = -1.832863267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.728571429' to each side of the equation. -1.728571429 + 1.728571429 + x = -1.832863267 + 1.728571429 Combine like terms: -1.728571429 + 1.728571429 = 0.000000000 0.000000000 + x = -1.832863267 + 1.728571429 x = -1.832863267 + 1.728571429 Combine like terms: -1.832863267 + 1.728571429 = -0.104291838 x = -0.104291838 Simplifying x = -0.104291838Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.561434696, -0.104291838}
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