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Simplifying 5x2 + -13 + 14x = 0 Reorder the terms: -13 + 14x + 5x2 = 0 Solving -13 + 14x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 2.8x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 2.8x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 2.8x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 2.8x + x2 = 0 + 2.6 2.8x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 2.8x + x2 = 2.6 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 2.6 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 2.6 + 1.96 Combine like terms: 2.6 + 1.96 = 4.56 1.96 + 2.8x + x2 = 4.56 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 4.56 Calculate the square root of the right side: 2.13541565 Break this problem into two subproblems by setting (x + 1.4) equal to 2.13541565 and -2.13541565.Subproblem 1
x + 1.4 = 2.13541565 Simplifying x + 1.4 = 2.13541565 Reorder the terms: 1.4 + x = 2.13541565 Solving 1.4 + x = 2.13541565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 2.13541565 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 2.13541565 + -1.4 x = 2.13541565 + -1.4 Combine like terms: 2.13541565 + -1.4 = 0.73541565 x = 0.73541565 Simplifying x = 0.73541565Subproblem 2
x + 1.4 = -2.13541565 Simplifying x + 1.4 = -2.13541565 Reorder the terms: 1.4 + x = -2.13541565 Solving 1.4 + x = -2.13541565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -2.13541565 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -2.13541565 + -1.4 x = -2.13541565 + -1.4 Combine like terms: -2.13541565 + -1.4 = -3.53541565 x = -3.53541565 Simplifying x = -3.53541565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.73541565, -3.53541565}
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