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Simplifying 4x2 + 19x + -29 = 0 Reorder the terms: -29 + 19x + 4x2 = 0 Solving -29 + 19x + 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'. -7.25 + 4.75x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + 4.75x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + 4.75x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + 4.75x + x2 = 0 + 7.25 4.75x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 4.75x + x2 = 7.25 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 7.25 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 7.25 + 5.640625 Combine like terms: 7.25 + 5.640625 = 12.890625 5.640625 + 4.75x + x2 = 12.890625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 12.890625 Calculate the square root of the right side: 3.590351654 Break this problem into two subproblems by setting (x + 2.375) equal to 3.590351654 and -3.590351654.Subproblem 1
x + 2.375 = 3.590351654 Simplifying x + 2.375 = 3.590351654 Reorder the terms: 2.375 + x = 3.590351654 Solving 2.375 + x = 3.590351654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 3.590351654 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 3.590351654 + -2.375 x = 3.590351654 + -2.375 Combine like terms: 3.590351654 + -2.375 = 1.215351654 x = 1.215351654 Simplifying x = 1.215351654Subproblem 2
x + 2.375 = -3.590351654 Simplifying x + 2.375 = -3.590351654 Reorder the terms: 2.375 + x = -3.590351654 Solving 2.375 + x = -3.590351654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -3.590351654 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -3.590351654 + -2.375 x = -3.590351654 + -2.375 Combine like terms: -3.590351654 + -2.375 = -5.965351654 x = -5.965351654 Simplifying x = -5.965351654Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.215351654, -5.965351654}
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