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Simplifying 5x2 + 14x + -374 = 0 Reorder the terms: -374 + 14x + 5x2 = 0 Solving -374 + 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'. -74.8 + 2.8x + x2 = 0 Move the constant term to the right: Add '74.8' to each side of the equation. -74.8 + 2.8x + 74.8 + x2 = 0 + 74.8 Reorder the terms: -74.8 + 74.8 + 2.8x + x2 = 0 + 74.8 Combine like terms: -74.8 + 74.8 = 0.0 0.0 + 2.8x + x2 = 0 + 74.8 2.8x + x2 = 0 + 74.8 Combine like terms: 0 + 74.8 = 74.8 2.8x + x2 = 74.8 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 = 74.8 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 74.8 + 1.96 Combine like terms: 74.8 + 1.96 = 76.76 1.96 + 2.8x + x2 = 76.76 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 76.76 Calculate the square root of the right side: 8.761278446 Break this problem into two subproblems by setting (x + 1.4) equal to 8.761278446 and -8.761278446.Subproblem 1
x + 1.4 = 8.761278446 Simplifying x + 1.4 = 8.761278446 Reorder the terms: 1.4 + x = 8.761278446 Solving 1.4 + x = 8.761278446 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 = 8.761278446 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 8.761278446 + -1.4 x = 8.761278446 + -1.4 Combine like terms: 8.761278446 + -1.4 = 7.361278446 x = 7.361278446 Simplifying x = 7.361278446Subproblem 2
x + 1.4 = -8.761278446 Simplifying x + 1.4 = -8.761278446 Reorder the terms: 1.4 + x = -8.761278446 Solving 1.4 + x = -8.761278446 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 = -8.761278446 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -8.761278446 + -1.4 x = -8.761278446 + -1.4 Combine like terms: -8.761278446 + -1.4 = -10.161278446 x = -10.161278446 Simplifying x = -10.161278446Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.361278446, -10.161278446}
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