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Simplifying 10x2 + -14x + -3 = 0 Reorder the terms: -3 + -14x + 10x2 = 0 Solving -3 + -14x + 10x2 = 0 Solving for variable 'x'. 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 = 1.588819442 x = 1.588819442 Simplifying x = 1.588819442Subproblem 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 = -0.188819442 x = -0.188819442 Simplifying x = -0.188819442Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.588819442, -0.188819442}
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