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Simplifying 4x2 + -29 + 5x + 1 = 0 Reorder the terms: -29 + 1 + 5x + 4x2 = 0 Combine like terms: -29 + 1 = -28 -28 + 5x + 4x2 = 0 Solving -28 + 5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7 + 1.25x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 1.25x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 1.25x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 1.25x + x2 = 0 + 7 1.25x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 1.25x + x2 = 7 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 7 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 7 + 0.390625 Combine like terms: 7 + 0.390625 = 7.390625 0.390625 + 1.25x + x2 = 7.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 7.390625 Calculate the square root of the right side: 2.718570396 Break this problem into two subproblems by setting (x + 0.625) equal to 2.718570396 and -2.718570396.Subproblem 1
x + 0.625 = 2.718570396 Simplifying x + 0.625 = 2.718570396 Reorder the terms: 0.625 + x = 2.718570396 Solving 0.625 + x = 2.718570396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 2.718570396 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 2.718570396 + -0.625 x = 2.718570396 + -0.625 Combine like terms: 2.718570396 + -0.625 = 2.093570396 x = 2.093570396 Simplifying x = 2.093570396Subproblem 2
x + 0.625 = -2.718570396 Simplifying x + 0.625 = -2.718570396 Reorder the terms: 0.625 + x = -2.718570396 Solving 0.625 + x = -2.718570396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -2.718570396 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -2.718570396 + -0.625 x = -2.718570396 + -0.625 Combine like terms: -2.718570396 + -0.625 = -3.343570396 x = -3.343570396 Simplifying x = -3.343570396Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.093570396, -3.343570396}
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