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Simplifying 10x2 + 14x = 3 Reorder the terms: 14x + 10x2 = 3 Solving 14x + 10x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 14x + 10x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 14x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 1.4x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 1.4x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 1.4x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 1.4x + x2 = 0 + 0.3 1.4x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 1.4x + x2 = 0.3 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 0.3 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 0.3 + 0.49 Combine like terms: 0.3 + 0.49 = 0.79 0.49 + 1.4x + x2 = 0.79 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 0.79 Calculate the square root of the right side: 0.888819442 Break this problem into two subproblems by setting (x + 0.7) equal to 0.888819442 and -0.888819442.Subproblem 1
x + 0.7 = 0.888819442 Simplifying x + 0.7 = 0.888819442 Reorder the terms: 0.7 + x = 0.888819442 Solving 0.7 + x = 0.888819442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 0.888819442 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.888819442 + -0.7 x = 0.888819442 + -0.7 Combine like terms: 0.888819442 + -0.7 = 0.188819442 x = 0.188819442 Simplifying x = 0.188819442Subproblem 2
x + 0.7 = -0.888819442 Simplifying x + 0.7 = -0.888819442 Reorder the terms: 0.7 + x = -0.888819442 Solving 0.7 + x = -0.888819442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -0.888819442 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.888819442 + -0.7 x = -0.888819442 + -0.7 Combine like terms: -0.888819442 + -0.7 = -1.588819442 x = -1.588819442 Simplifying x = -1.588819442Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.188819442, -1.588819442}
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