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Simplifying 2x(7x + 5) = 13 + -3x Reorder the terms: 2x(5 + 7x) = 13 + -3x (5 * 2x + 7x * 2x) = 13 + -3x (10x + 14x2) = 13 + -3x Solving 10x + 14x2 = 13 + -3x Solving for variable 'x'. Reorder the terms: -13 + 10x + 3x + 14x2 = 13 + -3x + -13 + 3x Combine like terms: 10x + 3x = 13x -13 + 13x + 14x2 = 13 + -3x + -13 + 3x Reorder the terms: -13 + 13x + 14x2 = 13 + -13 + -3x + 3x Combine like terms: 13 + -13 = 0 -13 + 13x + 14x2 = 0 + -3x + 3x -13 + 13x + 14x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -13 + 13x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.9285714286 + 0.9285714286x + x2 = 0 Move the constant term to the right: Add '0.9285714286' to each side of the equation. -0.9285714286 + 0.9285714286x + 0.9285714286 + x2 = 0 + 0.9285714286 Reorder the terms: -0.9285714286 + 0.9285714286 + 0.9285714286x + x2 = 0 + 0.9285714286 Combine like terms: -0.9285714286 + 0.9285714286 = 0.0000000000 0.0000000000 + 0.9285714286x + x2 = 0 + 0.9285714286 0.9285714286x + x2 = 0 + 0.9285714286 Combine like terms: 0 + 0.9285714286 = 0.9285714286 0.9285714286x + x2 = 0.9285714286 The x term is 0.9285714286x. Take half its coefficient (0.4642857143). Square it (0.2155612245) and add it to both sides. Add '0.2155612245' to each side of the equation. 0.9285714286x + 0.2155612245 + x2 = 0.9285714286 + 0.2155612245 Reorder the terms: 0.2155612245 + 0.9285714286x + x2 = 0.9285714286 + 0.2155612245 Combine like terms: 0.9285714286 + 0.2155612245 = 1.1441326531 0.2155612245 + 0.9285714286x + x2 = 1.1441326531 Factor a perfect square on the left side: (x + 0.4642857143)(x + 0.4642857143) = 1.1441326531 Calculate the square root of the right side: 1.069641367 Break this problem into two subproblems by setting (x + 0.4642857143) equal to 1.069641367 and -1.069641367.Subproblem 1
x + 0.4642857143 = 1.069641367 Simplifying x + 0.4642857143 = 1.069641367 Reorder the terms: 0.4642857143 + x = 1.069641367 Solving 0.4642857143 + x = 1.069641367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + x = 1.069641367 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + x = 1.069641367 + -0.4642857143 x = 1.069641367 + -0.4642857143 Combine like terms: 1.069641367 + -0.4642857143 = 0.6053556527 x = 0.6053556527 Simplifying x = 0.6053556527Subproblem 2
x + 0.4642857143 = -1.069641367 Simplifying x + 0.4642857143 = -1.069641367 Reorder the terms: 0.4642857143 + x = -1.069641367 Solving 0.4642857143 + x = -1.069641367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + x = -1.069641367 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + x = -1.069641367 + -0.4642857143 x = -1.069641367 + -0.4642857143 Combine like terms: -1.069641367 + -0.4642857143 = -1.5339270813 x = -1.5339270813 Simplifying x = -1.5339270813Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6053556527, -1.5339270813}
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