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Simplifying 0 = 5x2 + -14x + 3 Reorder the terms: 0 = 3 + -14x + 5x2 Solving 0 = 3 + -14x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + 14x + -5x2 = 3 + -14x + 5x2 + -3 + 14x + -5x2 Reorder the terms: -3 + 14x + -5x2 = 3 + -3 + -14x + 14x + 5x2 + -5x2 Combine like terms: 3 + -3 = 0 -3 + 14x + -5x2 = 0 + -14x + 14x + 5x2 + -5x2 -3 + 14x + -5x2 = -14x + 14x + 5x2 + -5x2 Combine like terms: -14x + 14x = 0 -3 + 14x + -5x2 = 0 + 5x2 + -5x2 -3 + 14x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -3 + 14x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.6 + -2.8x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2.8x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2.8x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2.8x + x2 = 0 + -0.6 -2.8x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2.8x + x2 = -0.6 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 = -0.6 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = -0.6 + 1.96 Combine like terms: -0.6 + 1.96 = 1.36 1.96 + -2.8x + x2 = 1.36 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (x + -1.4) equal to 1.166190379 and -1.166190379.Subproblem 1
x + -1.4 = 1.166190379 Simplifying x + -1.4 = 1.166190379 Reorder the terms: -1.4 + x = 1.166190379 Solving -1.4 + x = 1.166190379 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 = 1.166190379 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.166190379 + 1.4 x = 1.166190379 + 1.4 Combine like terms: 1.166190379 + 1.4 = 2.566190379 x = 2.566190379 Simplifying x = 2.566190379Subproblem 2
x + -1.4 = -1.166190379 Simplifying x + -1.4 = -1.166190379 Reorder the terms: -1.4 + x = -1.166190379 Solving -1.4 + x = -1.166190379 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 = -1.166190379 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.166190379 + 1.4 x = -1.166190379 + 1.4 Combine like terms: -1.166190379 + 1.4 = 0.233809621 x = 0.233809621 Simplifying x = 0.233809621Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.566190379, 0.233809621}
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