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Simplifying 5x2 + -12x + -29 = 5 Reorder the terms: -29 + -12x + 5x2 = 5 Solving -29 + -12x + 5x2 = 5 Solving for variable 'x'. Reorder the terms: -29 + -5 + -12x + 5x2 = 5 + -5 Combine like terms: -29 + -5 = -34 -34 + -12x + 5x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -34 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.8 + -2.4x + x2 = 0 Move the constant term to the right: Add '6.8' to each side of the equation. -6.8 + -2.4x + 6.8 + x2 = 0 + 6.8 Reorder the terms: -6.8 + 6.8 + -2.4x + x2 = 0 + 6.8 Combine like terms: -6.8 + 6.8 = 0.0 0.0 + -2.4x + x2 = 0 + 6.8 -2.4x + x2 = 0 + 6.8 Combine like terms: 0 + 6.8 = 6.8 -2.4x + x2 = 6.8 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 6.8 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 6.8 + 1.44 Combine like terms: 6.8 + 1.44 = 8.24 1.44 + -2.4x + x2 = 8.24 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 8.24 Calculate the square root of the right side: 2.870540019 Break this problem into two subproblems by setting (x + -1.2) equal to 2.870540019 and -2.870540019.Subproblem 1
x + -1.2 = 2.870540019 Simplifying x + -1.2 = 2.870540019 Reorder the terms: -1.2 + x = 2.870540019 Solving -1.2 + x = 2.870540019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 2.870540019 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.870540019 + 1.2 x = 2.870540019 + 1.2 Combine like terms: 2.870540019 + 1.2 = 4.070540019 x = 4.070540019 Simplifying x = 4.070540019Subproblem 2
x + -1.2 = -2.870540019 Simplifying x + -1.2 = -2.870540019 Reorder the terms: -1.2 + x = -2.870540019 Solving -1.2 + x = -2.870540019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -2.870540019 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.870540019 + 1.2 x = -2.870540019 + 1.2 Combine like terms: -2.870540019 + 1.2 = -1.670540019 x = -1.670540019 Simplifying x = -1.670540019Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.070540019, -1.670540019}
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