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Simplifying 4x2 + 29 = -28x Reorder the terms: 29 + 4x2 = -28x Solving 29 + 4x2 = -28x Solving for variable 'x'. Reorder the terms: 29 + 28x + 4x2 = -28x + 28x Combine like terms: -28x + 28x = 0 29 + 28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.25 + 7x + x2 = 0 Move the constant term to the right: Add '-7.25' to each side of the equation. 7.25 + 7x + -7.25 + x2 = 0 + -7.25 Reorder the terms: 7.25 + -7.25 + 7x + x2 = 0 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + 7x + x2 = 0 + -7.25 7x + x2 = 0 + -7.25 Combine like terms: 0 + -7.25 = -7.25 7x + x2 = -7.25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -7.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -7.25 + 12.25 Combine like terms: -7.25 + 12.25 = 5 12.25 + 7x + x2 = 5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 3.5) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 3.5 = 2.236067978 Simplifying x + 3.5 = 2.236067978 Reorder the terms: 3.5 + x = 2.236067978 Solving 3.5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.236067978 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.236067978 + -3.5 x = 2.236067978 + -3.5 Combine like terms: 2.236067978 + -3.5 = -1.263932022 x = -1.263932022 Simplifying x = -1.263932022Subproblem 2
x + 3.5 = -2.236067978 Simplifying x + 3.5 = -2.236067978 Reorder the terms: 3.5 + x = -2.236067978 Solving 3.5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.236067978 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.236067978 + -3.5 x = -2.236067978 + -3.5 Combine like terms: -2.236067978 + -3.5 = -5.736067978 x = -5.736067978 Simplifying x = -5.736067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.263932022, -5.736067978}
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