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Simplifying 5x2 + 14x = 7 Reorder the terms: 14x + 5x2 = 7 Solving 14x + 5x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 14x + 5x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 2.8x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 2.8x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 2.8x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 2.8x + x2 = 0 + 1.4 2.8x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 2.8x + x2 = 1.4 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 = 1.4 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 1.4 + 1.96 Combine like terms: 1.4 + 1.96 = 3.36 1.96 + 2.8x + x2 = 3.36 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (x + 1.4) equal to 1.833030278 and -1.833030278.Subproblem 1
x + 1.4 = 1.833030278 Simplifying x + 1.4 = 1.833030278 Reorder the terms: 1.4 + x = 1.833030278 Solving 1.4 + x = 1.833030278 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 = 1.833030278 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 1.833030278 + -1.4 x = 1.833030278 + -1.4 Combine like terms: 1.833030278 + -1.4 = 0.433030278 x = 0.433030278 Simplifying x = 0.433030278Subproblem 2
x + 1.4 = -1.833030278 Simplifying x + 1.4 = -1.833030278 Reorder the terms: 1.4 + x = -1.833030278 Solving 1.4 + x = -1.833030278 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 = -1.833030278 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -1.833030278 + -1.4 x = -1.833030278 + -1.4 Combine like terms: -1.833030278 + -1.4 = -3.233030278 x = -3.233030278 Simplifying x = -3.233030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.433030278, -3.233030278}
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