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Simplifying 2x(7x + -5) = 13 Reorder the terms: 2x(-5 + 7x) = 13 (-5 * 2x + 7x * 2x) = 13 (-10x + 14x2) = 13 Solving -10x + 14x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -10x + 14x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -10x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.9285714286 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.9285714286' to each side of the equation. -0.9285714286 + -0.7142857143x + 0.9285714286 + x2 = 0 + 0.9285714286 Reorder the terms: -0.9285714286 + 0.9285714286 + -0.7142857143x + x2 = 0 + 0.9285714286 Combine like terms: -0.9285714286 + 0.9285714286 = 0.0000000000 0.0000000000 + -0.7142857143x + x2 = 0 + 0.9285714286 -0.7142857143x + x2 = 0 + 0.9285714286 Combine like terms: 0 + 0.9285714286 = 0.9285714286 -0.7142857143x + x2 = 0.9285714286 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 0.9285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 0.9285714286 + 0.1275510204 Combine like terms: 0.9285714286 + 0.1275510204 = 1.056122449 0.1275510204 + -0.7142857143x + x2 = 1.056122449 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 1.056122449 Calculate the square root of the right side: 1.027678184 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.027678184 and -1.027678184.Subproblem 1
x + -0.3571428572 = 1.027678184 Simplifying x + -0.3571428572 = 1.027678184 Reorder the terms: -0.3571428572 + x = 1.027678184 Solving -0.3571428572 + x = 1.027678184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.027678184 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.027678184 + 0.3571428572 x = 1.027678184 + 0.3571428572 Combine like terms: 1.027678184 + 0.3571428572 = 1.3848210412 x = 1.3848210412 Simplifying x = 1.3848210412Subproblem 2
x + -0.3571428572 = -1.027678184 Simplifying x + -0.3571428572 = -1.027678184 Reorder the terms: -0.3571428572 + x = -1.027678184 Solving -0.3571428572 + x = -1.027678184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.027678184 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.027678184 + 0.3571428572 x = -1.027678184 + 0.3571428572 Combine like terms: -1.027678184 + 0.3571428572 = -0.6705353268 x = -0.6705353268 Simplifying x = -0.6705353268Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3848210412, -0.6705353268}
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