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Simplifying 5x2 + 7x + -29 = 0 Reorder the terms: -29 + 7x + 5x2 = 0 Solving -29 + 7x + 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'. -5.8 + 1.4x + x2 = 0 Move the constant term to the right: Add '5.8' to each side of the equation. -5.8 + 1.4x + 5.8 + x2 = 0 + 5.8 Reorder the terms: -5.8 + 5.8 + 1.4x + x2 = 0 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + 1.4x + x2 = 0 + 5.8 1.4x + x2 = 0 + 5.8 Combine like terms: 0 + 5.8 = 5.8 1.4x + x2 = 5.8 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 = 5.8 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 5.8 + 0.49 Combine like terms: 5.8 + 0.49 = 6.29 0.49 + 1.4x + x2 = 6.29 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 6.29 Calculate the square root of the right side: 2.507987241 Break this problem into two subproblems by setting (x + 0.7) equal to 2.507987241 and -2.507987241.Subproblem 1
x + 0.7 = 2.507987241 Simplifying x + 0.7 = 2.507987241 Reorder the terms: 0.7 + x = 2.507987241 Solving 0.7 + x = 2.507987241 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 = 2.507987241 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 2.507987241 + -0.7 x = 2.507987241 + -0.7 Combine like terms: 2.507987241 + -0.7 = 1.807987241 x = 1.807987241 Simplifying x = 1.807987241Subproblem 2
x + 0.7 = -2.507987241 Simplifying x + 0.7 = -2.507987241 Reorder the terms: 0.7 + x = -2.507987241 Solving 0.7 + x = -2.507987241 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 = -2.507987241 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -2.507987241 + -0.7 x = -2.507987241 + -0.7 Combine like terms: -2.507987241 + -0.7 = -3.207987241 x = -3.207987241 Simplifying x = -3.207987241Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.807987241, -3.207987241}
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